1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
| <template>
| <div class="chapter" num="4">
| <!-- 第三单元首页 -->
| <div class="page-box" page="74">
| <div v-if="showPageList.indexOf(74) > -1">
| <h1 id="a007"><img class="img-0" alt="" src="../../assets/images/dy3.jpg" /></h1>
| <div class="padding-116">
| <p>
| 在客观世界中存在各种各样的运动变化现象.如搭载神舟十四号载人飞船的长征二号运载火箭发射过程中，飞船与发射点距离会随着时间的变化而变化；深海勇士号载人潜水器在下潜实验过程中，其压强随着下潜深度的增加而增大；代表新能源技术的光伏发电和风能发电，我国的装机容量随时间变化而增长；我国快速发展的高速铁路，其总里程是逐年增加的，现已突破4万km
| ，稳居世界第一；每个人的体温随着时间的变化而变化；到商店购买同一种饮料的数量越多，付费越多等.这些动态变化现象都表现为变量之间的对应关系，我们常用函数模型来描述这些变量之间的关系和规律，并通过研究函数来认识客观世界.
| </p>
| <p>函数是描述客观世界变化规律和解决数学问题的重要工具.它与代数式、方程、不等式等知识联系紧密，是进一步学习数学的重要基础.函数的概念及其反映的数学思想和方法已广泛渗透到数学的各个领域，并在现实生活中有着广泛的应用.
| </p>
| <p>
| 本单元主要学习函数的概念、函数的表示方法、函数的单调性和奇偶性以及函数的应用.本单元的学习，重在感受用直观想象从具体问题中抽象出数学问题，并用精确的数学符号语言表达概念、性质、推理等；掌握研究函数的基本内容、过程和方法；运用建立分段函数、二次函数等数学模型解决实际问题的方法；积累一定的数学经验和方法，提升直观想象、数学抽象、数学建模、逻辑推理等核心素养.
| </p>
| </div>
| </div>
| </div>
| <!-- 目标 -->
| <div class="page-box" page="75">
| <div v-if="showPageList.indexOf(75) > -1">
| <div class="padding-116">
| <p class="left"><img class="inline2" alt="" src="../../assets/images/xxmb.jpg" /></p>
| <div class="fieldset">
| <p>1.函数的概念.</p>
| <p>能从具体情境中抽象概括出函数的概念，学习用集合语言和对应关系描述函数概念.</p>
| <p>2.函数的表示方法.</p>
| <p>了解函数的三种表示方法，会恰当地选用这些方法表示函数；</p>
| <p>理解分段函数的概念；</p>
| <p>通过研究函数的变化规律来把握客观世界中事物的变化规律.</p>
| <p>3.函数的单调性和奇偶性.</p>
| <p>学习用精准的数学符号语言描述函数的性质，掌握判断函数单调性和奇偶性的方法.</p>
| <p>4.函数的应用.</p>
| <p>初步掌握建立分段函数、二次函数模型来解决实际问题的方法；</p>
| <p>能运用函数的思想和方法解决实际问题，提升核心素养和思维品质.</p>
| </div>
| </div>
| </div>
| </div>
| <!-- 069 -->
| <div class="page-box" page="76">
| <div v-if="showPageList.indexOf(76) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>069</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <h2 id="b015">3.1 函数的概念<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" /></p>
| <p>情境1：职业教育助力乡村振兴，某职业院校电子商务专业学生小莉负责帮助某村农户在电商平台上销售2 000 kg橘子，橘子的售价是6元/kg.考查橘子的销售收入<i>y</i>（元） 与销售量<i>x</i>（kg）
| 的关系.
| </p>
| <p>情境2：如表3-1所示，2007年4月至2020年7月，我国共成功发射了55颗北斗导航卫星，全面建成了我国自主建设、独立运行的北斗卫星导航系统.考查每年发射卫星的颗数<i>y</i>与年份<i>x</i>的关系.
| </p>
| <p class="img">表3-1</p>
| <p class="center"><img class="img-a" alt="" src="../../assets/images/0080-1.jpg" /></p>
| <p>情境3：为了建设人与自然和谐共生的美丽家园，气温变化是环境监测的重要内容，某城市某年7月某一天的气温如图3-1所示.描述这一天气温的变化情况，考查温度<i>Q</i>与时间<i>t</i>的关系.</p>
| <p class="center"><img class="img-d" alt="" src="../../assets/images/0080-2.jpg" /></p>
| <p class="img">图3-1</p>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" /></p>
| <p>情境1中，橘子的销售收入<i>y</i>与销售量<i>x</i>的对应关系是<i>y</i>=6<i>x</i>，其中<i>x</i>的变化范围是数集<i>A</i>={<i>x</i>|0≤<i>x</i>≤2
| 000}，<i>y</i>的取值都在数集<i>B</i>={<i>y</i>|0≤<i>y</i>≤12
| 000}中，对于数集<i>A</i>中的任一销售量<i>x</i>，在数集<i>B</i>中都有唯一确定的收入<i>y</i>与之对应，所以橘子的销售收入<i>y</i>是销售量<i>x</i>的函数.</p>
| <p>
| 情境2中，<i>x</i>表示年份，<i>y</i>表示发射卫星颗数，<i>x</i>的变化范围是数集<i>A</i>={2007，
| </p>
| </div>
| </div>
| </div>
| <!-- 070 -->
| <div class="page-box" page="77">
| <div v-if="showPageList.indexOf(77) > -1">
| <ul class="page-header-odd fl al-end">
| <li>070</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <p class="t0">
| 2009，2010，2011，2012，2015，2016，2017，2018，2019，2020}，<i>y</i>的变化范围是数集<i>B</i>={1，2，3，4，5，6，10，18}，对于数集<i>A</i>中的任一年份<i>x</i>，根据表3-1所给定的对应关系，在数集<i>B</i>中都有唯一确定的卫星颗数<i>y</i>与之对应，因此，每年发射卫星颗数<i>y</i>是年份<i>x</i>的函数.
| </p>
| <p>
| 情境3中，<i>t</i>的变化范围是数集<i>A</i>={<i>x</i>|0≤<i>t</i>≤24}，<i>Q</i>的取值都在数集<i>B</i>={<i>Q</i>|22≤<i>Q</i>≤32}中，对于数集<i>A</i>中的任一时刻<i>t</i>，按照图3-1中曲线给出的对应关系，在数集<i>B</i>中都有唯一确定的气温<i>Q</i>与之对应，所以气温<i>Q</i>是时间<i>t</i>的函数.
| </p>
| <p>在现实生活中，这样的例子还有很多.比如，每小时往蓄水池里注入2 <i>t</i>水，蓄水池的水位与注水时间的对应关系；火车匀速直线行驶的路程与行驶时间的对应关系等.</p>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" /></p>
| <p>一般地，设<i>A</i>，<i>B</i>是非空数集， 如果存在一个对应关系<i>f</i>，使对于集合 <i>A</i> 中的每一个数<i>x</i>，在集合<i>B</i> 中都有唯一确定的数<i>y</i>
| 和它对应，那么就把对应关系<i>f</i>称为定义在集合<i>A</i>上的一个<b>函数</b>，记作</p>
| <p class="center"><i>y</i>=<i>f</i>（<i>x</i>），<i>x</i>∈<i>A</i>.</p>
| <p>
| 其中，<i>x</i>叫作<b>自变量</b>，<i>x</i>的取值范围<i>A</i>叫作函数的<b>定义域</b>；与<i>x</i>的值相对应的<i>y</i>值叫作函数值，函数值的集合{<i>f</i>（<i>x</i>）|<i>x</i>∈<i>A</i>}叫作函数的<b>值域</b>.
| </p>
| <p>
| 比如，初中学习过的一次函数<i>y</i>=3<i>x</i>-2，就是从实数集<b>R</b>（集合<i>A</i>）按照对应关系<i>f</i>（<i>x</i>）=3<i>x</i>-2到实数集<b>R</b>（集合<i>B</i>）的一个函数；二次函数<i>y</i>=<i>x</i><sup>2</sup>+4<i>x</i>-3，就是从实数集<b>R</b>（集合<i>A</i>）按照对应关系<i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+4<i>x</i>-3到实数集{<i>y</i>|<i>y</i>≥-7}（集合<i>B</i>）的一个函数.
| </p>
| <p>
| 对于函数<i>y</i>=<i>f</i>（<i>x</i>），当自变量在定义域内取一个确定的值<i>a</i>时，相应的函数值记作<i>f</i>（<i>a</i>）.例如，函数<i>y</i>=<i>f</i>（<i>x</i>）=3<i>x</i>，当<i>x</i>=3，其函数值是<i>f</i>（3）=3×3=9.
| </p>
| <div class="bk">
| <div class="bj1">
| <p class="left"><img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" /></p>
| </div>
| <p class="block">
| 函数符号<i>f</i>（<i>x</i>）中的<i>f</i>表示函数关系，不同的函数中，<i>f</i>的含义不同，函数的符号还常用<i>g</i>（<i>x</i>），<i>h</i>（<i>x</i>），<i>φ</i>（<i>x</i>），<i>F</i>（<i>x</i>）等表示.自变量除用<i>x</i>表示外，也常用<i>t</i>，<i>u</i>，<i>v</i>等表示.
| </p>
| </div>
| </div>
| </div>
| </div>
| <!-- 071 -->
| <div class="page-box" page="78">
| <div v-if="showPageList.indexOf(78) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>071</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <p class="p-btn" >
| <span>
| <span
| class="zt-ls"><b>例1</b></span> 我国要建设现代化产业体系，推动制造业高端化发展.李平制作了6个机械零件，它们的直径如表3-2所示.请用函数的概念描述李平制作这批机械零件的直径<i>y</i>（<i>mm</i>
| ）与零件的标号<i>x</i>的函数关系.
| </span>
| <span class="btn-box" @click="isShowAnswer0 = !isShowAnswer0">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <p class="img">表3-2</p>
| <p class="center"><img class="img-a" alt="" src="../../assets/images/0082-1.jpg" /></p>
| <p v-if="isShowAnswer0" >
| <span class="zt-ls"><b>解</b></span>
| 设<i>x</i>表示零件的标号，<i>y</i>表示零件的直径，由表3-2，{1，2，3，4，5，6}中的任一数，<i>y</i>都有任一确定的值与它对应，所以表3-2确定了<i>y</i>与<i>x</i>的函数关系，其定义域为{1，2，3，4，5，6}，值域为{13.40，13.50，13.55，13.60，13.65，13.70}.
| </p>
| <p class="p-btn" >
| <span>
| <span
| class="zt-ls"><b>例2</b></span> 已知函数<i>f</i>（<i>x</i>）=3<i>x</i><sup>2</sup>-1.当自变量<i>x</i>为-1，0，1，<i>a</i>时，求它们所对应的函数值.
| </span>
| <span class="btn-box" @click="isShowAnswer1 = !isShowAnswer1">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer1" >
| <p><span class="zt-ls"><b>解</b></span> <i>f</i>（-1）=3×（-1）<sup>2</sup>-1=3-1=2，</p>
| <p> <i>f</i>（0）=3×0<sup>2</sup>-1=0-1=-1，</p>
| <p> <i>f</i>（1）=3×1<sup>2</sup>-1=3-1=2，</p>
| <p> <i>f</i>（<i>a</i>）=3×<i>a</i><sup>2</sup>-1=3<i>a</i><sup>2</sup>-1.</p>
| </div>
| <div class="fieldset">
| <p><b>相关链接</b></p>
| <p class="block">魔方是由6个不同颜色的面组成的正方体，它可组成约4 325亿亿种不同颜色的组合，其最佳复原魔方颜色组合的方法是用数学方法研究出来的.</p>
| </div>
| <div class="bk-hzjl">
| <div class="bj1-hzjl">
| <p class="left">
| <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
| </p>
| </div>
| <examinations :cardList="questionData[78] ? questionData[78][1] : []" sourceType="json" v-if="questionData">
| </examinations>
| </div>
| <p class="center"><img class="img-c" alt="" src="../../assets/images/0082-2.jpg" /></p>
| <p class="img">图3-2</p>
| <p>
| <span>
| <span class="zt-ls"><b>例3</b></span> 如图3-2所示，一个边长是<i>a</i>的正方体，体积是<i>V</i>，写出体积<i>V</i> 随边长<i>a</i>
| 变化的函数关系式，并指出函数的自变量和定义域.
| </span>
| <span class="btn-box" @click="isShowAnswer2 = !isShowAnswer2">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer2" >
| <p><span class="zt-ls"><b>解</b></span> 体积<i>V</i> 随边长<i>a</i>变化的函数关系式是</p>
| <p class="center"><i>V</i>=<i>a</i><sup>3</sup>（<i>a</i>＞0）.</p>
| <p>其中<i>a</i>是自变量，定义域为{<i>a</i>|<i>a</i>＞0}.</p>
| </div>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
| <div class="bj">
| <examinations :cardList="questionData[78] ? questionData[78][2] : []" sourceType="json" inputBc="#d3edfa"
| v-if="questionData" ></examinations>
| </div>
| </div>
| </div>
| </div>
| <!-- 072 -->
| <div class="page-box" page="79">
| <div v-if="showPageList.indexOf(79) > -1">
| <ul class="page-header-odd fl al-end">
| <li>072</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <div class="bj">
| <p>（3） 若函数<i>f</i>（<i>x</i>）=2<i>x</i>-1，则<i>f</i>（<i>t</i>）=___，<i>f</i>（<i>f</i>（5））=____.</p>
| <p>2.一列动车从A城以每小时200km的速度匀速直线行驶4 h后到达B城.该动车在行驶过程中，行驶的路程是时间的函数吗？如果是，请写出函数的定义域、对应关系和值域；如果不是，请说明理由.</p>
| </div>
| <p>从上面的学习可以知道，一个函数包含定义域、对应关系和值域.函数的值域是由函数的定义域和对应关系决定的.</p>
| <p>通常函数的定义域隐含在函数关系中.例如，我们不能计算当<i>x</i>=0时<math display="0">
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <mfrac>
| <mn>1</mn>
| <mi>x</mi>
| </mfrac>
| </math>的函数值<i>f</i>（0），因为<i>f</i>（0）无意义，因此，它的定义域是{<i>x</i>｜<i>x</i>≠0}.在实际问题中，函数的定义域通常由问题的实际背景所决定.如例3中的函数<i>V</i>=<i>a</i><sup>3</sup>，由于<i>a</i>是正方体的边长，所以函数的定义域为<i>A</i>={<i>a</i>｜<i>a</i>＞0}.
| </p>
| <p class="p-btn" >
| <span>
| <span
| class="zt-ls"><b>例4</b></span> 就业是最基本的民生，小凯通过自主创办奶品店实现职业发展.为促销自制酸奶，每瓶酸奶的价格是3.5元，每位顾客最多只能购买50瓶.假设某人购买这种酸奶<i>x</i>瓶，应付款<i>y</i>元.那么<i>y</i>（元）是<i>x</i>（瓶）的函数吗？如果是，请写出函数的定义域、对应关系和值域；如果不是，请说明理由.
| </span>
| <span class="btn-box" @click="isShowAnswer3 = !isShowAnswer3">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer3" >
| <p><span class="zt-ls"><b>解</b></span>
| <i>x</i>的取值范围是数集<i>A</i>={<i>x</i>|<i>x</i>≤50，<i>x</i>∈<b>N</b>}，<i>y</i>的取值范围是数集<i>B</i>={<i>y</i>|<i>y</i>=3.5<i>x</i>，<i>x</i>≤50，且<i>x</i>∈<b>N</b>}.对于集合<i>A</i>中的任一个数<i>x</i>，按照对应关系，在集合<i>B</i>中都有唯一确定的值与之对应，所以应付款<i>y</i>是购买数量<i>x</i>的函数.
| </p>
| <p>
| 函数的定义域是{<i>x</i>|<i>x</i>≤50，<i>x</i>∈<b>N</b>}，对应关系是<i>y</i>=3.5<i>x</i>，值域是{<i>y</i>|<i>y</i>=3.5<i>x</i>，<i>x</i>≤50，且<i>x</i>∈<b>N</b>}.
| </p>
| <p>
| 例4中函数的定义域为什么是{<i>x</i>|<i>x</i>≤50，<i>x</i>∈<b>N</b>}，而不是{<i>x</i>|<i>x</i>∈<b>R</b>}？这是因为此函数的定义域考虑了函数自变量取值的客观实际背景.
| </p>
| </div>
| <p class="center"><img class="img-c" alt="" src="../../assets/images/0083-2.jpg" /></p>
| <p class="img">图3-3</p>
| <p class="p-btn" >
| <span>
| <span
| class="zt-ls"><b>例5</b></span> 如图3-3所示，在矩形<i>ABCD</i>中，<i>AB</i>的长度是<i>x</i>（m），<i>BC</i>的长度是（12-<i>x</i>）（m），矩形<i>ABCD</i>的面积是<i>y</i>（<i>m</i><sup>2</sup>），则<i>y</i>与<i>x</i>的对应关系是<i>y</i>=<i>x</i>（12-<i>x</i>），求该函数的定义域.
| </span>
| <span class="btn-box" @click="isShowAnswer4 = !isShowAnswer4">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| <span class="btn-box" @click="openDialog(thinkTwo)">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
| <path class="a"
| d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
| transform="translate(-3761 14334.001)" />
| </svg>
| </span>
| </p>
| <p v-if="isShowAnswer4" >
| <span class="zt-ls"><b>解</b></span> 要使函数<i>y</i>=<i>x</i>（12-<i>x</i>）有实际意义，必须满足<math display="0">
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">{</mo>
| <mtable columnspacing="1em" rowspacing="4pt">
| <mtr>
| <mtd>
| <mi>x</mi>
| <mo>＞</mo>
| <mn>0</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| </mtr>
| <mtr>
| <mtd>
| <mn>12</mn>
| <mo>−</mo>
| <mi>x</mi>
| <mo>＞</mo>
| <mn>0</mn>
| </mtd>
| <mtd></mtd>
| </mtr>
| </mtable>
| <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
| </mrow>
| </math>解得0＜<i>x</i>＜12.所以这个函数的定义域是{<i>x</i>|0＜<i>x</i>＜12}.</p>
| </div>
| </div>
| </div>
| <!-- 073 -->
| <div class="page-box" page="80">
| <div v-if="showPageList.indexOf(80) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>073</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <p><span class="zt-ls"><b>例6</b></span> 求下列函数的定义域.</p>
| <p class="p-btn" >
| <span>
| （1） <math display="0">
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <mfrac>
| <mn>1</mn>
| <mrow>
| <mn>4</mn>
| <mi>x</mi>
| <mo>+</mo>
| <mn>7</mn>
| </mrow>
| </mfrac>
| </math>；
| </span>
| <span class="btn-box" @click="isShowAnswer5 = !isShowAnswer5">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer5" >
| <p><span class="zt-ls"><b>解</b></span>（1） 要使该函数有意义，必须满足</p>
| <p class="center">4<i>x</i>+7≠0，</p>
| <p>解得</p>
| <math display="block">
| <mi>x</mi>
| <mo>≠</mo>
| <mo>−</mo>
| <mfrac>
| <mn>7</mn>
| <mn>4</mn>
| </mfrac>
| <mo>.</mo>
| </math>
| <p>所以函数<i>f</i>（<i>x</i>）的定义域是<math display="0">
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">{</mo>
| <mi>x</mi>
| <mrow>
| <mo stretchy="false">|</mo>
| </mrow>
| <mi>x</mi>
| <mo>≠</mo>
| <mo>−</mo>
| <mfrac>
| <mn>7</mn>
| <mn>4</mn>
| </mfrac>
| <mo data-mjx-texclass="CLOSE">}</mo>
| </mrow>
| </math>.</p>
| </div>
| <p class="p-btn">
| <span>
| （2）<math display="0">
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <msqrt>
| <mi>x</mi>
| <mo>−</mo>
| <mn>3</mn>
| </msqrt>
| </math>；
| </span>
| <span class="btn-box" @click="isShowAnswer6 = !isShowAnswer6">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer6" >
| <p> <span class="zt-ls"><b>解</b></span>（2） 要使该函数有意义，必须满足</p>
| <p class="center"><i>x</i>-3≥0，</p>
| <p>解得 <i>x</i>≥3.</p>
| <p>所以函数<i>f</i>（<i>x</i>）的定义域是{<i>x</i>|<i>x</i>≥3}.</p>
| </div>
| <p class="p-btn" >
| <span>
| （3） <math display="0">
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <msqrt>
| <mn>4</mn>
| <mi>x</mi>
| <mo>+</mo>
| <mn>8</mn>
| </msqrt>
| <mo>+</mo>
| <mfrac>
| <mn>1</mn>
| <mrow>
| <mi>x</mi>
| <mo>−</mo>
| <mn>3</mn>
| </mrow>
| </mfrac>
| </math>.
| </span>
| <span class="btn-box" @click="isShowAnswer7 = !isShowAnswer7">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer7" >
| <p> <span class="zt-ls"><b>解</b></span>（3） 要使该函数有意义，必须满足</p>
| <math display="block">
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">{</mo>
| <mtable columnspacing="1em" rowspacing="4pt">
| <mtr>
| <mtd>
| <mn>4</mn>
| <mi>x</mi>
| <mo>+</mo>
| <mn>8</mn>
| <mo>≥</mo>
| <mn>0</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| </mtr>
| <mtr>
| <mtd>
| <mi>x</mi>
| <mo>−</mo>
| <mn>3</mn>
| <mo>≠</mo>
| <mn>0</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| </mtr>
| </mtable>
| <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
| </mrow>
| </math>
| <p>解得</p>
| <math display="block">
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">{</mo>
| <mtable columnspacing="1em" rowspacing="4pt">
| <mtr>
| <mtd>
| <mi>x</mi>
| <mo>≥</mo>
| <mo>−</mo>
| <mn>2</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| </mtr>
| <mtr>
| <mtd>
| <mi>x</mi>
| <mo>≠</mo>
| <mn>3.</mn>
| </mtd>
| <mtd></mtd>
| </mtr>
| </mtable>
| <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
| </mrow>
| </math>
| <p>所以函数<i>f</i>（<i>x</i>）的定义域是{<i>x</i>|<i>x</i>≥-2且<i>x</i>≠3}.</p>
| </div>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
| <div class="bj" >
| <examinations :cardList="questionData[80]" sourceType="json" inputBc="#d3edfa"
| v-if="questionData" ></examinations>
| </div>
| </div>
| </div>
| </div>
| <!-- 074 -->
| <div class="page-box" page="81">
| <div v-if="showPageList.indexOf(81) > -1">
| <ul class="page-header-odd fl al-end">
| <li>074-076</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <h3 id="c026">习题3.1<span class="fontsz2">＞＞＞</span></h3>
| <div class="bj" >
| <examinations :cardList="questionData[81]" sourceType="json" inputBc="#d3edfa"
| v-if="questionData" ></examinations>
| </div>
| <h2 id="b016">3.2 函数的表示方法<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
| <h3 id="c027">3.2.1 函数的表示方法<span class="fontsz2">＞＞＞</span></h3>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" /></p>
| <p>我们知道，上一节“观察思考”中的3个情境都涉及变量之间的函数关系.情境1中，销售收入<i>y</i>（元）与销售量<i>x</i>（kg ）的函数关系是<i>y</i>=6<i>x</i>，0≤<i>x</i>≤2
| 000，这种表示函数关系的方法称为解析法；情境2中，用表格表示了发射卫星的颗数<i>y</i>与年份<i>x</i>的函数关系，这种表示函数关系的方法称为列表法；情境3中，用图像表示了气温<i>Q</i>与时间<i>t</i>的函数关系，这种表示函数关系的方法称为图像法.
| </p>
| <p class="p-btn" >
| <span>
| <span class="zt-ls"><b>例1</b></span> 某辆汽车以30 km/<i>h</i> 的速度匀速直线行驶，用解析法表示汽车行驶的路程<i>s</i>（km
| ）与时间<i>t</i>（<i>h</i>）之间的对应关系.
| </span>
| <span class="btn-box" @click="isShowAnswer8 = !isShowAnswer8">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer8" >
| <p><span class="zt-ls"><b>解</b></span> 这个函数的定义域是{<i>t</i>|<i>t</i>≥0}.</p>
| <p>用解析法可将这个函数表示为<i>s</i>=30<i>t</i>，<i>t</i>≥0.</p>
| <p>用解析法表示函数关系，能够准确、完整地反映两个变量之间的关系.</p>
| </div>
| <p>
| <span>
| <span class="zt-ls"><b>例2</b></span> 近年我国快递业务量迅速增长，从2017年至2021年，每年的快递业务量情况如表3-4所示（注：引自国家统计局数据）.
| </span>
| <span class="btn-box" @click="isShowAnswer9 = !isShowAnswer9">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <p class="img">表3-4</p>
| <p class="center"><img class="img-a" alt="" src="../../assets/images/0087-2.jpg" /></p>
| <p v-if="isShowAnswer9" >表3-4清晰地反映了年份与当年快递业务量（亿件）之间的对应关系.在实际生活中，用列表法表示变量之间对应关系的例子还有很多.例如，记录某人每天的消费情况、单位职工的每月薪资收入、银行使用的存款“利息表”等.</p>
| </div>
| </div>
| </div>
| <!-- 075 -->
| <div class="page-box hidePage" page="82">
| </div>
| <!-- 076 -->
| <div class="page-box hidePage" page="83">
| </div>
| <!-- 077 -->
| <div class="page-box" page="84">
| <div v-if="showPageList.indexOf(84) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>077</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <div v-if="isShowAnswer9" >
| <p>观察上一节“观察思考”中的情境3，我们发现用图像法表示函数关系时能直观形象地表示出函数的局部变化规律，进而可以预测它的整体变化趋势.但是我们并不能作出所有函数的图像.</p>
| </div>
| <p>
| <span>
| <span
| class="zt-ls"><b>例3</b></span> 使用环保毛巾替代一次性纸巾，是倡导低碳环保生活的一种方式.某便民超市促销某种小毛巾，每条售价4元，每人限购5条.若顾客购买<i>x</i>条小毛巾需要付款<i>y</i>元，试用图像法表示函数<i>y</i>=<i>f</i>（<i>x</i>）.
| </span>
| <span class="btn-box" @click="isShowAnswer10 = !isShowAnswer10">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer10" >
| <p><span class="zt-ls"><b>解</b></span> 函数<i>y</i>=<i>f</i>（<i>x</i>）的定义域是{1，2，3，4，5}，用图像法可将这个函数表示为图3-4.</p>
| <p class="center"><img class="img-c" alt="" src="../../assets/images/0088-1.jpg" /></p>
| <p class="img">图3-4</p>
| <p>
| 函数的图像既可以是离散的点，也可以是线段、直线、折线、连续的曲线等.在初中，我们用列表、描点、连线的方法画出了正比例函数、反比例函数、一次函数和二次函数的图像.图像法也被大量用于各类数据统计中.例如，GDP（国内生产总值）每年的增长情况、居民消费价格每季度的增长情况、全国人口数量每年的变化情况等.
| </p>
| </div>
| <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
| <p>
| <span>
| <span class="zt-ls"><b>例4</b></span> 一艘军舰与某海港相距135 n mile（1 n mile ≈1.852 km ），如果军舰以45 n mile/h 的速度向海港前行，则3
| h后可到达海港.假设这艘军舰出发t（h）后，与海港的距离是s（n mile）.
| </span>
| <span class="btn-box" @click="openDialog(thinkThree)">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
| <path class="a"
| d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
| transform="translate(-3761 14334.001)" />
| </svg>
| </span>
| </p>
| <p class="p-btn" >
| <span>
| （1） 用解析法表示函数<i>s</i>=<i>f</i>（<i>t</i>）；
| </span>
| <span class="btn-box" @click="isShowAnswer11 = !isShowAnswer11">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer11" >
| <p><span class="zt-ls"><b>解</b></span>（1） 因为该军舰从出发地驶入海港需要用时<math display="0">
| <mfrac>
| <mn>135</mn>
| <mn>45</mn>
| </mfrac>
| <mo>=</mo>
| <mn>3</mn>
| <mo>（</mo>
| <mi>h</mi>
| <mo>）</mo>
| </math>，所以函数的定义域为{<i>t</i>|0≤<i>t</i>≤3}.
| </p>
| <p>又因为该军舰出发<i>t</i>（<i>h</i>）后，行驶的路程为45<i>t n mile</i> ，这时该军舰与海港的距离为（135-45<i>t</i>） <i>n mile</i> .</p>
| <p>所以，用解析法可将函数<i>s</i>=<i>f</i>（<i>t</i>）表示为</p>
| <p class="center"><i>s</i>=-45<i>t</i>+135，0≤<i>t</i>≤3.</p>
| </div>
| <p class="p-btn" >
| <span>（2） 用图像法表示函数<i>s</i>=<i>f</i>（<i>t</i>）.</span>
| <span class="btn-box" @click="isShowAnswer12 = !isShowAnswer12">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer12" >
| <p> <span class="zt-ls"><b>解</b></span>（2） 函数<i>s</i>=<i>f</i>（<i>t</i>）是一次函数，用图像法可将函数表示为图3-5.</p>
| <p class="center"><img class="img-c" alt="" src="../../assets/images/0088-3.jpg" /></p>
| <p class="img">图3-5</p>
| </div>
| </div>
| </div>
| </div>
| <!-- 078 -->
| <div class="page-box" page="85">
| <div v-if="showPageList.indexOf(85) > -1">
| <ul class="page-header-odd fl al-end">
| <li>078</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <div class="bk-hzjl">
| <div class="bj1-hzjl">
| <p class="left"><img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" /></p>
| </div>
| <examinations :cardList="questionData[85] ? questionData[85][1] : []" sourceType="json" inputBc="#d3edfa"
| v-if="questionData" ></examinations>
| </div>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
| <div class="bj">
| <examinations :cardList="questionData[85] ? questionData[85][2] : []" sourceType="json" inputBc="#d3edfa"
| v-if="questionData" ></examinations>
| </div>
| </div>
| </div>
| </div>
| <!-- 079 -->
| <div class="page-box" page="86">
| <div v-if="showPageList.indexOf(86) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>079</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <h3 id="c028">3.2.2 分段函数<span class="fontsz2">＞＞＞</span></h3>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" /></p>
| <p>城市轨道交通出行便利，拉近了人们的距离.某城市地铁的票价如表3-6所示.1号线地铁全长21 km .设某位乘客乘坐的地铁行驶的路程为<i>x</i>（km
| ），票价是<i>y</i>（元），则<i>y</i>是<i>x</i>的函数，你能写出这个函数的解析式吗？</p>
| <p class="img">表3-6</p>
| <p class="center"><img class="img-a" alt="" src="../../assets/images/0090-1.jpg" /></p>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" /></p>
| <p>
| 从表3-6可以发现，当0＜<i>x</i>≤6时，<i>y</i>=2；当6＜<i>x</i>≤11时，<i>y</i>=3；当11＜<i>x</i>≤16时，<i>y</i>=4；当16＜<i>x</i>≤21时，<i>y</i>=5.该函数的解析式如下.
| </p>
| <math display="block">
| <mi>y</mi>
| <mo>=</mo>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">{</mo>
| <mtable columnspacing="1em" rowspacing="4pt">
| <mtr>
| <mtd>
| <mn>2</mn>
| <mo>，</mo>
| <mn>0</mn>
| <mo>＜</mo>
| <mi>x</mi>
| <mo>≤</mo>
| <mn>6</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| <mtd></mtd>
| <mtd></mtd>
| </mtr>
| <mtr>
| <mtd>
| <mn>3</mn>
| <mo>，</mo>
| <mn>6</mn>
| <mo>＜</mo>
| <mi>x</mi>
| <mo>≤</mo>
| <mn>11</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| <mtd></mtd>
| <mtd></mtd>
| </mtr>
| <mtr>
| <mtd>
| <mn>4</mn>
| <mo>，</mo>
| <mn>11</mn>
| <mo>＜</mo>
| <mi>x</mi>
| <mo>≤</mo>
| <mn>16</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| <mtd></mtd>
| <mtd></mtd>
| </mtr>
| <mtr>
| <mtd>
| <mn>5</mn>
| <mo>，</mo>
| <mn>16</mn>
| <mo>＜</mo>
| <mi>x</mi>
| <mo>≤</mo>
| <mn>21</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| <mtd></mtd>
| <mtd></mtd>
| </mtr>
| </mtable>
| <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
| </mrow>
| </math>
| <div class="bk">
| <div class="bj1">
| <p class="left"><img class="img-gn1" alt="" src="../../assets/images/gn.jpg" /></p>
| </div>
| <p class="block">分段函数</p>
| </div>
| <p class="center"><img class="img-c" alt="" src="../../assets/images/0090-4.jpg" /></p>
| <p class="img">图3-6</p>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" /></p>
| <p>像上面的函数，在自变量不同的取值范围内，有不同的对应关系，这样的函数叫作<b>分段函数</b>.</p>
| <p>
| 例如，函数<i>y</i>=|<i>x</i>|的图像如图3-6所示.根据绝对值的概念，当<i>x</i>≥0时，<i>y</i>=<i>x</i>；当<i>x</i>＜0时，<i>y</i>=-<i>x</i>.所以这个函数的解析式为
| </p>
| <math display="block">
| <mi>y</mi>
| <mo>=</mo>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">{</mo>
| <mtable columnspacing="1em" rowspacing="4pt">
| <mtr>
| <mtd>
| <mi>x</mi>
| <mo>，</mo>
| <mi>x</mi>
| <mo>≥</mo>
| <mn>0</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| <mtd></mtd>
| <mtd></mtd>
| </mtr>
| <mtr>
| <mtd>
| <mo>−</mo>
| <mi>x</mi>
| <mo>，</mo>
| <mi>x</mi>
| <mo>＜</mo>
| <mn>0.</mn>
| </mtd>
| <mtd></mtd>
| <mtd></mtd>
| <mtd></mtd>
| </mtr>
| </mtable>
| <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
| </mrow>
| </math>
| <p>生活中有很多可以用分段函数来描述的实际问题，如出租车计费，每个家庭水、电、燃气的计费，综合所得税纳税额等.</p>
| <p><span class="zt-ls"><b>例1</b></span> 已知函数<math display="0">
| <mi>y</mi>
| <mo>=</mo>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">{</mo>
| <mtable columnspacing="1em" rowspacing="4pt">
| <mtr>
| <mtd>
| <mi>x</mi>
| <mo>+</mo>
| <mn>2</mn>
| <mo>，</mo>
| <mi>x</mi>
| <mo>≤</mo>
| <mn>0</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| <mtd></mtd>
| <mtd></mtd>
| </mtr>
| <mtr>
| <mtd>
| <msup>
| <mi>x</mi>
| <mrow>
| <mn>2</mn>
| </mrow>
| </msup>
| <mo>−</mo>
| <mn>3</mn>
| <mo>，</mo>
| <mi>x</mi>
| <mo>＞</mo>
| <mn>0.</mn>
| </mtd>
| <mtd></mtd>
| <mtd></mtd>
| <mtd></mtd>
| </mtr>
| </mtable>
| <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
| </mrow>
| </math></p>
| <p class="p-btn" >
| <span>
| （1） 求<i>f</i>（-5），<i>f</i>（4）的值；
| </span>
| <span class="btn-box" @click="isShowAnswer13 = !isShowAnswer13">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer13" >
| <p><span class="zt-ls"><b>解</b></span>（1） 因为-5＜0，所以<i>f</i>（-5）=-5+2=-3.</p>
| <p>因为4＞0，所以 <i>f</i>（4）=4<sup>2</sup>-3=13.</p>
| </div>
| </div>
| </div>
| </div>
| <!-- 080 -->
| <div class="page-box" page="87">
| <div v-if="showPageList.indexOf(87) > -1">
| <ul class="page-header-odd fl al-end">
| <li>080</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <p class="p-btn" >
| <span>（2） 求<i>f</i>（<i>f</i>（-1））的值.</span>
| <span class="btn-box" @click="isShowAnswer14 = !isShowAnswer14">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer14">
| <p> <span class="zt-ls"><b>解</b></span>（2） 因为-1＜0，所以<i>f</i>（-1）=-1+2=1.</p>
| <p>又因为1＞0，所以<i>f</i>（<i>f</i>（-1））=<i>f</i>（1）=1<sup>2</sup>-3=-2.</p>
| </div>
| <div class="bk">
| <div class="bj1">
| <p class="left"><img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" /></p>
| </div>
| <p class="block">
| 分段函数是一个函数，不能把它看成几个函数，只是在同一个函数的定义域内，不同的取值范围内对应不同的函数关系.它的定义域是各个解析式的自变量取值集合的并集，值域也是各个解析式的函数值集合的并集.它的图像也比较特殊，有时图像是不连续的.
| </p>
| </div>
| <p>
| <span
| class="zt-ls"><b>例2</b></span> 我国是用电量最大的国家，国家发出节能减排的号召，鼓励居民节约用电，2019年国家对居民每月用电量进行划分，电价施行“分档递增”.某城市居民每月用电计费价格如表3-7所示.假设这个城市的某居民某月用电量是<i>x</i>（kW·h），需支付电费<i>y</i>（元）.
| <span class="btn-box" @click="openDialog(thinkFour)">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
| <path class="a"
| d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
| transform="translate(-3761 14334.001)" />
| </svg>
| </span>
| </p>
| <p class="img">表3-7 某城市居民每月用电计费价格表</p>
| <p class="center"><img class="img-a" alt="" src="../../assets/images/0091-1.jpg" /></p>
| <p class="p-btn" >
| <span>（1） 用解析法表示<i>y</i>与<i>x</i>的函数关系，并画出函数的图像.</span>
| <span class="btn-box" @click="isShowAnswer15 = !isShowAnswer15">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer15" >
| <p><span class="zt-ls"><b>解</b></span>（1） 函数<i>y</i>=<i>f</i>（<i>x</i>）的定义域是{<i>x</i>|<i>x</i>≥0}.</p>
| <p>当0≤<i>x</i>≤200时，<i>y</i>与<i>x</i>的对应关系是<i>y</i>=0.52<i>x</i>；</p>
| <p>当200＜<i>x</i>≤400时，<i>y</i>与<i>x</i>的对应关系是</p>
| <p class="center"><i>y</i>=0.52×200+0.57（<i>x</i>-200）=0.57<i>x</i>-10；</p>
| <p>当<i>x</i>＞400时，<i>y</i>与<i>x</i>的对应关系是</p>
| <p><i>y</i>=0.52×200+0.57×200+0.82（<i>x</i>-400）=0.82<i>x</i>-110.</p>
| <p>用解析法表示<i>y</i>与<i>x</i>的函数关系如下.</p>
| <math display="block">
| <mi>y</mi>
| <mo>=</mo>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">{</mo>
| <mtable columnspacing="1em" rowspacing="4pt">
| <mtr>
| <mtd>
| <mn>0.52</mn>
| <mi>x</mi>
| <mo>，</mo>
| <mn>0</mn>
| <mo>≤</mo>
| <mi>x</mi>
| <mo>≤</mo>
| <mn>200</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| <mtd></mtd>
| <mtd></mtd>
| </mtr>
| <mtr>
| <mtd>
| <mn>0.57</mn>
| <mi>x</mi>
| <mo>−</mo>
| <mn>10</mn>
| <mo>，</mo>
| <mn>200</mn>
| <mo>＜</mo>
| <mi>x</mi>
| <mo>≤</mo>
| <mn>400</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| <mtd></mtd>
| <mtd></mtd>
| </mtr>
| <mtr>
| <mtd>
| <mn>0.82</mn>
| <mi>x</mi>
| <mo>−</mo>
| <mn>110</mn>
| <mo>，</mo>
| <mi>x</mi>
| <mo>＞</mo>
| <mn>400.</mn>
| </mtd>
| <mtd></mtd>
| <mtd></mtd>
| <mtd></mtd>
| </mtr>
| </mtable>
| <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
| </mrow>
| </math>
| <p class="center"><img class="img-c" alt="" src="../../assets/images/0092-1.jpg" /></p>
| <p class="img">图3-7</p>
| <p>这个函数的图像如图3-7所示.</p>
| </div>
| <p class="p-btn" >
| <span>（2） 如果李某家10月的用电量是180 kW·h ，那么他家应该支付电费多少？</span>
| <span class="btn-box" @click="isShowAnswer16 = !isShowAnswer16">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer16" >
| <p> <span class="zt-ls"><b>解</b></span>（2） 因为<i>x</i>=180＜200，<i>y</i>=0.52×180=93.60（元）.</p>
| <p>所以，李某家10月应该支付电费93.60元.</p>
| </div>
| <p class="p-btn" >
| <span>（3） 如果周某家12月支付电费294.26元，那么他家这个月的用电量是多少？</span>
| <span class="btn-box" @click="isShowAnswer17 = !isShowAnswer17">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer17" >
| <p> <span class="zt-ls"><b>解</b></span>（3） 周某家电费是294.26元，由图3-7可估得<i>x</i>＞400，因此</p>
| <p class="center">0.82<i>x</i>-110=294.26，</p>
| <p>解得<i>x</i>=493.</p>
| <p>所以，周某家12月的用电量为493 kW·h .</p>
| </div>
| </div>
| </div>
| </div>
| <!-- 081 -->
| <div class="page-box" page="88">
| <div v-if="showPageList.indexOf(88) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>081</span></p>
| </li>
| </ul>
| <div class="padding-116">
|
| <div class="bk-hzjl">
| <div class="bj1-hzjl">
| <p class="left"><img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" /></p>
| </div>
| <examinations :cardList="questionData[88] ? questionData[88][1] : []" sourceType="json"
| v-if="questionData" ></examinations>
| </div>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
| <div class="bj">
| <examinations :cardList="questionData[88] ? questionData[88][2] : []" sourceType="json" inputBc="#d3edfa"
| v-if="questionData" ></examinations>
| </div>
| </div>
| </div>
| </div>
| <!-- 082 -->
| <div class="page-box" page="89">
| <div v-if="showPageList.indexOf(89) > -1">
| <ul class="page-header-odd fl al-end">
| <li>082-084</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <h3 id="c029">习题3.2<span class="fontsz2">＞＞＞</span></h3>
| <div class="bj">
| <examinations :cardList="questionData[89]" sourceType="json" inputBc="#d3edfa"
| v-if="questionData" ></examinations>
| </div>
| <h2 id="b017">3.3 函数的单调性和奇偶性<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
| <h3 id="c030">3.3.1 函数的单调性<span class="fontsz2">＞＞＞</span></h3>
| <p>函数是描述事物运动变化规律的模型，我们可以通过研究函数的性质来把握客观世界中事物的变化规律.</p>
| <p>
| 比如，1970年4月24日我国发射了第一颗人造卫星“东方红一号”.2003年10月15日9：00，我国自行研制的“神舟”五号载人飞船在酒泉卫星发射中心成功发射升空，历时9时9分50秒后进入预定轨道，飞船绕地球飞行14圈，经过21小时23分钟后，于16日6：23载着英雄杨利伟成功着陆.在发射过程中，随着时间的变化，“长征”运载火箭飞行的高度越来越高；“神舟”五号飞船着陆过程中，随着时间的变化，飞船离地面的高度越来越低.发射升空的运载火箭（或着陆的载人飞船）离地面的高度是飞行时间的函数.科技工作者研究这些函数后，才能够把飞船按计划送入预定轨道或确保飞船安全着陆.这是我们认识客观规律的重要方法和途径.
| </p>
| </div>
| </div>
| </div>
| <!-- 083 -->
| <div class="page-box hidePage" page="90">
| </div>
| <!-- 084 -->
| <div class="page-box hidePage" page="91">
| </div>
| <!-- 085 -->
| <div class="page-box" page="92">
| <div v-if="showPageList.indexOf(92) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>085</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" /></p>
| <p>
| 在初中，我们曾经利用函数图像探究函数值<i>y</i>随着自变量<i>x</i>的增大而增大（或减小）的变化规律.仔细观察图3-8的函数图像，随着自变量<i>x</i>的增大，函数值<i>y</i>的变化趋势分别是怎样的？
| </p>
| <p class="center"><img class="img-b" alt="" src="../../assets/images/0096-1.jpg" /></p>
| <p class="img">图3-8</p>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" /></p>
| <p>观察图3-8，函数<i>y</i>=<i>x</i>和<i>y</i>=-<i>x</i>的定义域是<b>R</b>.当自变量<i>x</i>的值逐渐增大时，图3-8（1）
| 中，函数图像从左到右是上升的，函数值<i>y</i>随着自变量<i>x</i>的增大而增大.图3-8（2） 中，函数图像从左到右是下降的，函数值<i>y</i>随着自变量<i>x</i>的增大而减小.图3-8（3）
| 中，函数<i>y</i>=<i>x</i><sup>2</sup>的定义域是<b>R</b>.可以看出，在（-∞，0）内，函数图像从左到右是下降的，函数值<i>y</i>随着自变量<i>x</i>的增大而减小；在（0，+∞）内，函数图像从左到右是上升的，函数值<i>y</i>随着自变量<i>x</i>的增大而增大.
| </p>
| <div class="bk">
| <div class="bj1">
| <p class="left"><img class="img-gn1" alt="" src="../../assets/images/gn.jpg" /></p>
| </div>
| <p class="block">单调性</p>
| <p class="block">增函数</p>
| <p class="block">减函数</p>
| <p class="block">单调区间</p>
| </div>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" /></p>
| <p>像上述情形，在某个区间内，函数值随自变量的增大而增大（或减小）的性质叫作函数的<b>单调性</b>.</p>
| <p>一般地，设函数的定义域为<i>D</i>，区间<i>A</i>⊆<i>D</i>.</p>
| <p>（1）
| 如果对任意<i>x</i><sub>1</sub>，<i>x</i><sub>2</sub>∈<i>A</i>，当<i>x</i>1＜<i>x</i>2时，都有<i>f</i>（<i>x</i><sub>1</sub>）＜<i>f</i>（<i>x</i><sub>2</sub>），那么就称函数<i>f</i>（<i>x</i>）在区间<i>A</i>上<b>单调递增</b>，如图3-9所示.特别地，当函数<i>f</i>（<i>x</i>）在它的定义域上单调递增时，我们就称它是<b>增函数</b>.
| </p>
| <p>（2）
| 如果对任意<i>x</i><sub>1</sub>，<i>x</i><sub>2</sub>∈<i>A</i>，当<i>x</i><sub>1</sub>＜<i>x</i><sub>2</sub>时，都有<i>f</i>（<i>x</i><sub>1</sub>）＞<i>f</i>（<i>x</i><sub>2</sub>），那么就称函数<i>f</i>（<i>x</i>）在区间<i>A</i>上<b>单调递减</b>，如图3-10所示.特别地，当函数<i>f</i>（<i>x</i>）在它的定义域上单调递减时，我们就称它是<b>减函数</b>.
| </p>
| </div>
| </div>
| </div>
| <!-- 086 -->
| <div class="page-box" page="93">
| <div v-if="showPageList.indexOf(93) > -1">
| <ul class="page-header-odd fl al-end">
| <li>086</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <p>
| 如果函数<i>y</i>=<i>f</i>（<i>x</i>）在区间<i>A</i>上单调递增或单调递减，那么就称函数<i>y</i>=<i>f</i>（<i>x</i>）在区间<i>A</i>上具有（严格的）单调性，并且区间<i>A</i>叫作函数<i>y</i>=<i>f</i>（<i>x</i>）的<b>单调区间</b>.
| </p>
| <p class="center"><img class="img-c" alt="" src="../../assets/images/0097-1.jpg" /></p>
| <p class="img">图3-9</p>
| <p class="center"><img class="img-c" alt="" src="../../assets/images/0097-2.jpg" /></p>
| <p class="img">图3-10</p>
| <p>
| 例如，图3-8中函数<i>y</i>=<i>x</i>是<b>R</b>上的增函数，区间（-∞，+∞）是函数<i>y</i>=<i>x</i>的增区间；函数<i>y</i>=-<i>x</i>是<b>R</b>上的减函数，区间（-∞，+∞）是函数<i>y</i>=-<i>x</i>的减区间；函数<i>y</i>=<i>x</i><sup>2</sup>在区间（-∞，0）上是减函数，在区间（0，+∞）上是增函数，区间（-∞，0）和（0，+∞）分别是函数<i>y</i>=<i>x</i><sup>2</sup>的减区间、增区间.
| </p>
| <p><span class="zt-ls"><b>例1</b></span> 图3-11是函数<i>y</i>=<i>f</i>（<i>x</i>），<i>x</i>∈［-1，8］的图像，根据图像回答下列问题.</p>
| <p class="p-btn" >
| <span>（1） 当<i>x</i>取何值时，函数值最大，最大值是多少？当<i>x</i>取何值时，函数值最小，最小值是多少？</span>
| <span class="btn-box" @click="isShowAnswer18 = !isShowAnswer18">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <p v-if="isShowAnswer18" ><span class="zt-ls"><b>解</b></span>（1） 由图可知，当<i>x</i>=2时，函数值最大，最大值是3；当<i>x</i>=6时，函数值最小，最小值是-3.</p>
| <p class="p-btn" >
| <span>（2） 说明该函数的单调区间及在每一个区间上的单调性.</span>
| <span class="btn-box" @click="isShowAnswer19 = !isShowAnswer19">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <p class="center"><img class="img-c" alt="" src="../../assets/images/0097-3.jpg" /></p>
| <p class="img">图3-11</p>
| <p v-if="isShowAnswer19" >
| <span class="zt-ls"><b>解</b></span>
| （2）
| 函数<i>y</i>=<i>f</i>（<i>x</i>）的单调区间有［-1，2］，［2，6］，［6，8］.函数<i>y</i>=<i>f</i>（<i>x</i>）在区间［-1，2］和［6，8］上都是增函数，在区间［2，6］上是减函数.
| </p>
| </div>
| </div>
| </div>
| <!-- 087 -->
| <div class="page-box" page="94">
| <div v-if="showPageList.indexOf(94) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>087</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <p class="center"><img class="img-c" alt="" src="../../assets/images/0098-1.jpg" /></p>
| <p class="img">图3-12</p>
| <p><span class="zt-ls"><b>例2</b></span> 二次函数<i>f</i>（<i>x</i>）=-<i>x</i><sup>2</sup>+2<i>x</i>+3的图像如图3-12所示.
| </p>
| <p class="p-btn" >
| <span>（1） 求函数<i>f</i>（<i>x</i>）的对称轴方程、顶点坐标；</span>
| <span class="btn-box" @click="isShowAnswer20 = !isShowAnswer20">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer20" >
| <p><span class="zt-ls"><b>解</b></span>（1） 二次函数<i>y</i>=<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>的对称轴方程是<math
| display="0">
| <mi>x</mi>
| <mo>=</mo>
| <mfrac>
| <mi>b</mi>
| <mrow>
| <mn>2</mn>
| <mi>a</mi>
| </mrow>
| </mfrac>
| </math>，顶点坐标是<math display="0">
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mo>−</mo>
| <mfrac>
| <mi>b</mi>
| <mrow>
| <mn>2</mn>
| <mi>a</mi>
| </mrow>
| </mfrac>
| <mo>，</mo>
| <mfrac>
| <mrow>
| <mn>4</mn>
| <mi>a</mi>
| <mi>c</mi>
| <mo>−</mo>
| <msup>
| <mi>b</mi>
| <mrow>
| <mn>2</mn>
| </mrow>
| </msup>
| </mrow>
| <mrow>
| <mn>4</mn>
| <mi>a</mi>
| </mrow>
| </mfrac>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| </math>，则</p>
| <math display="block">
| <mtable columnalign="left" columnspacing="1em" rowspacing="4pt">
| <mtr>
| <mtd>
| <mo>−</mo>
| <mfrac>
| <mi>b</mi>
| <mrow>
| <mn>2</mn>
| <mi>a</mi>
| </mrow>
| </mfrac>
| <mo>=</mo>
| <mo>−</mo>
| <mfrac>
| <mn>2</mn>
| <mrow>
| <mn>2</mn>
| <mo>×</mo>
| <mo stretchy="false">(</mo>
| <mo>−</mo>
| <mn>1</mn>
| <mo stretchy="false">)</mo>
| </mrow>
| </mfrac>
| <mo>=</mo>
| <mn>1，</mn>
| </mtd>
| </mtr>
| <mtr>
| <mtd>
| <mfrac>
| <mrow>
| <mn>4</mn>
| <mi>a</mi>
| <mi>c</mi>
| <mo>−</mo>
| <msup>
| <mi>b</mi>
| <mrow>
| <mn>2</mn>
| </mrow>
| </msup>
| </mrow>
| <mrow>
| <mn>4</mn>
| <mi>a</mi>
| </mrow>
| </mfrac>
| <mo>=</mo>
| <mfrac>
| <mrow>
| <mn>4</mn>
| <mo>×</mo>
| <mo stretchy="false">(</mo>
| <mo>−</mo>
| <mn>1</mn>
| <mo stretchy="false">)</mo>
| <mo>×</mo>
| <mn>3</mn>
| <mo>−</mo>
| <msup>
| <mn>2</mn>
| <mrow>
| <mn>2</mn>
| </mrow>
| </msup>
| </mrow>
| <mrow>
| <mn>4</mn>
| <mo>×</mo>
| <mo stretchy="false">(</mo>
| <mo>−</mo>
| <mn>1</mn>
| <mo stretchy="false">)</mo>
| </mrow>
| </mfrac>
| <mo>=</mo>
| <mn>4</mn>
| <mo>.</mo>
| </mtd>
| </mtr>
| </mtable>
| </math>
| <p>因此，函数<i>f</i>（<i>x</i>）的对称轴方程是<i>x</i>=1，顶点坐标是（1，4）.</p>
| </div>
| <p class="p-btn" >
| <span>（2） 找出函数<i>f</i>（<i>x</i>）的单调区间；</span>
| <span class="btn-box" @click="isShowAnswer21 = !isShowAnswer21">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <p v-if="isShowAnswer21" > <span class="zt-ls"><b>解</b></span>（2） 由图像可知，函数<i>f</i>（<i>x</i>）的增区间是（-∞，1］，减区间是［1，+∞）.</p>
| <p class="p-btn" >
| <span>（3） 当<i>x</i>∈［2，5］时，求函数<i>f</i>（<i>x</i>）的最大值和最小值.</span>
| <span class="btn-box" @click="isShowAnswer22 = !isShowAnswer22">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer22" >
| <p> <span class="zt-ls"><b>解</b></span>（3） 因为［2，5］⫋［1，+∞），且函数在区间［1，+∞）上是减函数，所以当<i>x</i>∈［2，5］时，</p>
| <p>函数<i>f</i>（<i>x</i>）的最大值是<i>f</i>（2）=-2<sup>2</sup>+2×2+3=3，</p>
| <p>函数<i>f</i>（<i>x</i>）的最小值是<i>f</i>（5）=-5<sup>2</sup>+2×5+3=-12.</p>
| </div>
| <div class="bk">
| <div class="bj1">
| <p class="left"><img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" /></p>
| </div>
| <p class="block">函数的单调性是对定义域内某个区间而言的.一个函数在其定义域上不一定具有单调性，但是在定义域内的子区间上可能具有单调性，这就是函数单调性的局部性质.</p>
| </div>
| <p class="p-btn" >
| <span>
| <span class="zt-ls"><b>例3</b></span> 判断函数<i>f</i>（<i>x</i>）=<i>x</i>+1在（-∞，+∞）上的单调性.
| </span>
| <span class="btn-box" @click="isShowAnswer23 = !isShowAnswer23">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer23" >
| <p><span class="zt-ls"><b>解</b></span>
| 任取<i>x</i><sub>1</sub>，<i>x</i><sub>2</sub>∈（-∞，+∞），且<i>x</i><sub>1</sub>＜<i>x</i><sub>2</sub>，那么</p>
| <p class="center">
| <i>f</i>（<i>x</i><sub>1</sub>）=<i>x</i><sub>1</sub>+1，<i>f</i>（<i>x</i><sub>2</sub>）=<i>x</i><sub>2</sub>+1，
| </p>
| <p>则</p>
| <p class="center">
| <i>f</i>（<i>x</i><sub>1</sub>）-<i>f</i>（<i>x</i><sub>2</sub>）=<i>x</i><sub>1</sub>+1-<i>x</i><sub>2</sub>-1=<i>x</i><sub>1</sub>-<i>x</i><sub>2</sub>＜0，
| </p>
| <p>
| 所以<i>f</i>（<i>x</i><sub>1</sub>）＜<i>f</i>（<i>x</i><sub>2</sub>），函数<i>f</i>（<i>x</i>）=<i>x</i>+1在（-∞，+∞）上是增函数.
| </p>
| <p>当<i>k</i>＞0时，函数<i>f</i>（<i>x</i>）=<i>kx</i>+<i>b</i>在区间（-∞，+∞）上是增函数，如图3-13（1）
| 所示；当<i>k</i>＜0时，函数<i>f</i>（<i>x</i>）=<i>kx</i>+<i>b</i>在区间（-∞，+∞）上是减函数，如图3-13（2） 所示.</p>
| <p class="center"><img class="img-b" alt="" src="../../assets/images/0098-5.jpg" /></p>
| <p class="img">图3-13</p>
| </div>
| <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
| </div>
| </div>
| </div>
| <!-- 088 -->
| <div class="page-box" page="95">
| <div v-if="showPageList.indexOf(95) > -1">
| <ul class="page-header-odd fl al-end">
| <li>088</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
| <div class="bj">
| <examinations :cardList="questionData[95]" sourceType="json" inputBc="#d3edfa"
| v-if="questionData" ></examinations>
| </div>
| </div>
| </div>
| </div>
| <!-- 089 -->
| <div class="page-box" page="96">
| <div v-if="showPageList.indexOf(96) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>089</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <h3 id="c031">
| 3.3.2 函数的奇偶性<span class="fontsz2">＞＞＞</span>
| </h3>
| <p class="left">
| <img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
| </p>
| <p>
| 函数<i>f</i>（<i>x</i>）=|<i>x</i>|和<i>g</i>（<i>x</i>）=<i>x</i><sup>2</sup>的图像的对称性如何？
| </p>
| <textarea cols="30" rows="4" v-model="chapterData.txtOne" placeholder="请输入内容" class="w100 ta-br textarea-text"
| @input="handleChapterData"></textarea>
| <p class="left">
| <img class="img-gn" alt="" src="../../assets/images/tjfx.jpg" />
| </p>
| <p>
| 列出表3-11和表3-12，画出函数<i>f</i>（<i>x</i>）=|<i>x</i>|
| 和<i>g</i>（<i>x</i>）=<i>x</i><sup>2</sup>的图像，如图3-14（1）
| 和（2） 所示.
| </p>
| <p class="img">表3-11</p>
| <p class="center">
| <img class="img-a" alt="" src="../../assets/images/0100-1.jpg" />
| </p>
| <p class="img">表3-12</p>
| <p class="center">
| <img class="img-a" alt="" src="../../assets/images/0100-2.jpg" />
| </p>
| <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
| <p class="center openImgBox">
| <img class="img-b" alt="" src="../../assets/images/0100-3.jpg" />
| </p>
| <p class="img">图3-14</p>
| <p>
| 观察图3-14（1）
| 发现，函数<i>f</i>（<i>x</i>）=|<i>x</i>|的定义域是（-∞，+∞），函数图像关于<i>y</i>轴对称.从表3-11中还发现，当自变量取一对相反数时，对应的函数值相等，如<i>f</i>（-1）=<i>f</i>（1）=1，<i>f</i>（-2）=<i>f</i>（2）=2，<i>f</i>（-3）=<i>f</i>（3）=3，…实际上，对任意<i>x</i>∈（-∞，+∞），都有<i>f</i>（-<i>x</i>）=|-<i>x</i>|=|<i>x</i>|=<i>f</i>（<i>x</i>），即<i>f</i>（-<i>x</i>）=<i>f</i>（<i>x</i>）.
| </p>
| <p>
| 图3-14（2）
| 中，函数<i>g</i>（<i>x</i>）=<i>x</i><sup>2</sup>的定义域是（-∞，+∞），函数图像也关于<i>y</i>轴对称.表3-12中，当自变量取一对相反数时，对应的函数值相等，如<i>g</i>（-1）=<i>g</i>（1）=1，<i>g</i>（-2）=<i>g</i>（2）=4，<i>g</i>（-3）=<i>g</i>（3）=9，…实际上，对任意<i>x</i>∈（-∞，+∞），都有<i>g</i>（-<i>x</i>）=（-<i>x</i>）<sup>2</sup>=<i>x</i><sup>2</sup>=<i>g</i>（<i>x</i>），即<i>g</i>（-<i>x</i>）=<i>g</i>（<i>x</i>）.
| </p>
| <p>
| 这两个函数的图像都关于 <i>y</i> 轴对称；当自变量取定义域中任意一对相
| </p>
| </div>
| </div>
| </div>
| <!-- 090 -->
| <div class="page-box" page="97">
| <div v-if="showPageList.indexOf(97) > -1">
| <ul class="page-header-odd fl al-end">
| <li>090</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <p class="t0">反数时，对应的函数值都相等，这种函数就是偶函数.</p>
| <p class="left">
| <img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
| </p>
| <p>
| 一般地，设函数<i>f</i>（<i>x</i>）的定义域为<i>D</i>，如果对于<span class="u">任意</span><i>x</i>∈<i>D</i>，<span
| class="u">都有</span>-<i>x</i>∈<i>D</i>，且<i>f</i>（-<i>x</i>）=<i>f</i>（<i>x</i>），那么函数<i>f</i>（<i>x</i>）就叫作<b>偶函数</b>，如图3-15所示.<b>偶函数的图像关于<i>y</i>轴对称</b>.
| </p>
| <p>
| 我们可以由函数的图像是否关于<i>y</i>轴对称来判断函数是不是偶函数.
| </p>
| <p class="center openImgBox">
| <img class="img-c" alt="" src="../../assets/images/0101-1.jpg" style="width: 40%" />
| </p>
| <p class="img fl fl-cn ju-cn">
| <span>图3-15</span>
| <img :src="collectResourceList.findIndex(item => item.id == '722FE833') > -1 ? collectCheck : collectImg"
| alt="" class="collect-btn" @click="handleCollect('img')" />
| </p>
| <video :src="videoPath" webkit-playsinline="true" x-webkit-airplay="true" playsinline="true"
| x5-video-orientation="h5" x5-video-player-fullscreen="true" x5-playsinline="" controls
| controlslist="nodownload" class="video-border w100"></video>
| <p class="img fl fl-cn ju-cn">
| <span>视频：判数函数奇偶性的方法和步骤 </span>
| <img
| :src="collectResourceList.findIndex(item => item.id == 'a28cd862d61b5df2201406b76e9f01b0') > -1 ? collectCheck : collectImg"
| alt="" class="collect-btn" @click="handleCollect('video')" />
| </p>
| <p class="fl">
| <span>
| <span class="zt-ls"><b>例1</b></span> 根据图3-16中函数的图像，判断哪些函数是偶函数.
| </span>
| <span class="btn-box" @click="isShowExampleOne = !isShowExampleOne">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <p class="center openImgBox">
| <img class="img-b" alt="" src="../../assets/images/0101-2.jpg" />
| </p>
| <p class="img">图3-16</p>
| <div v-if="isShowExampleOne">
| <p>
| <span class="zt-ls"><b>解</b></span> 在四个函数图像中，图3-16（1）
| 和图3-16（4） 的函数图像关于<i>y</i>轴对称；图3-16（2）
| 和图3-16（3）
| 的函数图像不关于<i>y</i>轴对称.根据偶函数的图像具有关于<i>y</i>轴对称的特点，图3-16（1）和图3-16（4）的函数是偶函数，图3-16（2）和图3-16（3）的函数不是偶函数.
| </p>
| </div>
| </div>
| </div>
| </div>
| <!-- 091 -->
| <div class="page-box" page="98">
| <div v-if="showPageList.indexOf(98) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>091</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <p class="fl">
| <span>
| <span class="zt-ls"><b>例2</b></span>
| 已知<i>f</i>（<i>x</i>）=|<i>x</i>|+1图像在<i>y</i>轴右边的部分如图3-17所示.试画出这个函数图像在<i>y</i>轴左边的部分.
| </span>
| <span class="btn-box" @click="isShowExampleTwo = !isShowExampleTwo">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <p class="center openImgBox">
| <img class="img-c" alt="" src="../../assets/images/0102-1.jpg" style="width: 40%" />
| </p>
| <p class="img">图3-17</p>
| <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
| <div v-if="isShowExampleTwo">
| <p>
| <span class="zt-ls"><b>解</b></span>
| 函数<i>f</i>（<i>x</i>）=|<i>x</i>|+1的定义域是（-∞，+∞），因为它是偶函数，所以根据其图像关于<i>y</i>轴对称的特点，即可画出这个函数在<i>x</i>∈（-∞，0］上的图像.
| </p>
| <p>
| 如图3-18所示，在<i>y</i>轴右边的图像上取两点<i>A</i>和<i>B</i>，分别画出它们关于<i>y</i>轴对称的点<i>A</i>′和<i>B</i>′，然后连线<i>A</i>′<i>B</i>′，就得到这个函数的图像在<i>y</i>轴左边的部分.
| </p>
| <p class="center openImgBox">
| <img class="img-c" alt="" src="../../assets/images/0102-2.jpg" style="width: 40%" />
| </p>
| <p class="img">图3-18</p>
| </div>
| <div class="bk">
| <div class="bj1">
| <p class="left">
| <img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
| </p>
| </div>
| <p class="block">
| 一个函数是不是偶函数，可以由函数的图像是否关于<i>y</i>轴对称来判断；当函数用解析法表示时，可以用偶函数的定义来判断.
| </p>
| </div>
| <p>
| <span class="zt-ls"><b>例3</b></span> 判断下列函数是不是偶函数.
| </p>
| <ul>
| <li class="fl fl-cn">
| <p>（1） <i>f</i>（<i>x</i>）=3<i>x</i><sup>2</sup>+1；</p>
| <span class="btn-box" @click="isShowExampleThree = !isShowExampleThree">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| <span class="btn-box" @click="openDialog(thinkOne)">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
| <path class="a"
| d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
| transform="translate(-3761 14334.001)" />
| </svg>
| </span>
| <span class="btn-box" @click="openMathDiaolog">
| <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="15.323"
| height="15.939" viewBox="0 0 18.323 15.939">
| <g transform="translate(-398 -946)">
| <path class="a"
| d="M11.985,1.241a.894.894,0,0,1-.242.623.79.79,0,0,1-.6.263.644.644,0,0,1-.547-.229,3.034,3.034,0,0,1-.339-.741A.935.935,0,0,0,10.1.846a.4.4,0,0,0-.291-.1.36.36,0,0,0-.333.18,1.836,1.836,0,0,0-.2.478L8.251,4.753H9.7l-.27.79H8.043l-1.51,4.849a27.9,27.9,0,0,1-1.06,2.93,5.5,5.5,0,0,1-1.316,1.857,3.11,3.11,0,0,1-2.189.755,2.258,2.258,0,0,1-1.455-.409A1.192,1.192,0,0,1,0,14.618a.97.97,0,0,1,.27-.693.894.894,0,0,1,.693-.291.741.741,0,0,1,.693.27,1.815,1.815,0,0,1,.2.693c0,.381.2.575.492.575a.817.817,0,0,0,.693-.478,6.983,6.983,0,0,0,.568-1.469L6,5.543H4.5l.236-.776h1.5l.159-.54a14.548,14.548,0,0,1,.693-2.016A4.544,4.544,0,0,1,8.313.694,2.91,2.91,0,0,1,10.281,0a2.425,2.425,0,0,1,.8.145,1.5,1.5,0,0,1,.693.429.963.963,0,0,1,.236.693Z"
| transform="translate(398 948)" />
| <path class="b"
| d="M18.323,5.668a3.505,3.505,0,0,1-.152,1.046H17.36a3.969,3.969,0,0,0,.166-1.06.5.5,0,0,0-.062-.236.27.27,0,0,0-.249-.132.346.346,0,0,0-.229.076c-.069.055-.222.208-.471.471L14.936,7.489a22.329,22.329,0,0,0-1.552,1.621l-1.815,1.974a2.168,2.168,0,0,1-1.385.859c-.492,0-.741-.333-.741-.991a3.575,3.575,0,0,1,.3-1.385h.914a4.766,4.766,0,0,0-.263,1.1c0,.18.048.263.159.263s.242-.111.464-.333l2.147-2.286c-.006-.033,1.525-1.611,1.524-1.6l1.3-1.385a2.078,2.078,0,0,1,1.385-.8.755.755,0,0,1,.776.388,1.9,1.9,0,0,1,.173.776Z"
| transform="translate(398 948)" />
| <path class="a"
| d="M14.936,7.489l.693,2.251a5.154,5.154,0,0,0,.236.61c.083.159.18.242.3.242a.82.82,0,0,0,.533-.457,4.849,4.849,0,0,0,.339-.817H17.8a4.849,4.849,0,0,1-.693,1.51,2.813,2.813,0,0,1-.873.852,1.766,1.766,0,0,1-.88.27,1.178,1.178,0,0,1-1.018-.464,4.357,4.357,0,0,1-.623-1.309l-.326-1.067a6.4,6.4,0,0,0-.222-.8L12.747,7c-.083-.27-.152-.478-.2-.6a1.136,1.136,0,0,0-.194-.312.4.4,0,0,0-.284-.118c-.326,0-.6.423-.817,1.261h-.769a6.671,6.671,0,0,1,.6-1.5,3.034,3.034,0,0,1,.81-.873,1.663,1.663,0,0,1,.942-.312,1.344,1.344,0,0,1,1.067.471,3.692,3.692,0,0,1,.644,1.268l.139.436C14.672,6.7,14.936,7.489,14.936,7.489Z"
| transform="translate(398 948)" />
| </g>
| </svg>
| </span>
| </li>
| <li class="fl fl-cn">
| <p>（2） <i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>；</p>
| <span class="btn-box" @click="isShowExampleFour = !isShowExampleFour">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| <span class="btn-box" @click="openMathDiaolog">
| <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="15.323"
| height="15.939" viewBox="0 0 18.323 15.939">
| <g transform="translate(-398 -946)">
| <path class="a"
| d="M11.985,1.241a.894.894,0,0,1-.242.623.79.79,0,0,1-.6.263.644.644,0,0,1-.547-.229,3.034,3.034,0,0,1-.339-.741A.935.935,0,0,0,10.1.846a.4.4,0,0,0-.291-.1.36.36,0,0,0-.333.18,1.836,1.836,0,0,0-.2.478L8.251,4.753H9.7l-.27.79H8.043l-1.51,4.849a27.9,27.9,0,0,1-1.06,2.93,5.5,5.5,0,0,1-1.316,1.857,3.11,3.11,0,0,1-2.189.755,2.258,2.258,0,0,1-1.455-.409A1.192,1.192,0,0,1,0,14.618a.97.97,0,0,1,.27-.693.894.894,0,0,1,.693-.291.741.741,0,0,1,.693.27,1.815,1.815,0,0,1,.2.693c0,.381.2.575.492.575a.817.817,0,0,0,.693-.478,6.983,6.983,0,0,0,.568-1.469L6,5.543H4.5l.236-.776h1.5l.159-.54a14.548,14.548,0,0,1,.693-2.016A4.544,4.544,0,0,1,8.313.694,2.91,2.91,0,0,1,10.281,0a2.425,2.425,0,0,1,.8.145,1.5,1.5,0,0,1,.693.429.963.963,0,0,1,.236.693Z"
| transform="translate(398 948)" />
| <path class="b"
| d="M18.323,5.668a3.505,3.505,0,0,1-.152,1.046H17.36a3.969,3.969,0,0,0,.166-1.06.5.5,0,0,0-.062-.236.27.27,0,0,0-.249-.132.346.346,0,0,0-.229.076c-.069.055-.222.208-.471.471L14.936,7.489a22.329,22.329,0,0,0-1.552,1.621l-1.815,1.974a2.168,2.168,0,0,1-1.385.859c-.492,0-.741-.333-.741-.991a3.575,3.575,0,0,1,.3-1.385h.914a4.766,4.766,0,0,0-.263,1.1c0,.18.048.263.159.263s.242-.111.464-.333l2.147-2.286c-.006-.033,1.525-1.611,1.524-1.6l1.3-1.385a2.078,2.078,0,0,1,1.385-.8.755.755,0,0,1,.776.388,1.9,1.9,0,0,1,.173.776Z"
| transform="translate(398 948)" />
| <path class="a"
| d="M14.936,7.489l.693,2.251a5.154,5.154,0,0,0,.236.61c.083.159.18.242.3.242a.82.82,0,0,0,.533-.457,4.849,4.849,0,0,0,.339-.817H17.8a4.849,4.849,0,0,1-.693,1.51,2.813,2.813,0,0,1-.873.852,1.766,1.766,0,0,1-.88.27,1.178,1.178,0,0,1-1.018-.464,4.357,4.357,0,0,1-.623-1.309l-.326-1.067a6.4,6.4,0,0,0-.222-.8L12.747,7c-.083-.27-.152-.478-.2-.6a1.136,1.136,0,0,0-.194-.312.4.4,0,0,0-.284-.118c-.326,0-.6.423-.817,1.261h-.769a6.671,6.671,0,0,1,.6-1.5,3.034,3.034,0,0,1,.81-.873,1.663,1.663,0,0,1,.942-.312,1.344,1.344,0,0,1,1.067.471,3.692,3.692,0,0,1,.644,1.268l.139.436C14.672,6.7,14.936,7.489,14.936,7.489Z"
| transform="translate(398 948)" />
| </g>
| </svg>
| </span>
| </li>
| <li class="fl fl-cn">
| <p>（3） <i>f</i>（<i>x</i>）=5<i>x</i>+2.</p>
| <span class="btn-box" @click="isShowExampleFive = !isShowExampleFive">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| <span class="btn-box" @click="openMathDiaolog">
| <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="15.323"
| height="15.939" viewBox="0 0 18.323 15.939">
| <g transform="translate(-398 -946)">
| <path class="a"
| d="M11.985,1.241a.894.894,0,0,1-.242.623.79.79,0,0,1-.6.263.644.644,0,0,1-.547-.229,3.034,3.034,0,0,1-.339-.741A.935.935,0,0,0,10.1.846a.4.4,0,0,0-.291-.1.36.36,0,0,0-.333.18,1.836,1.836,0,0,0-.2.478L8.251,4.753H9.7l-.27.79H8.043l-1.51,4.849a27.9,27.9,0,0,1-1.06,2.93,5.5,5.5,0,0,1-1.316,1.857,3.11,3.11,0,0,1-2.189.755,2.258,2.258,0,0,1-1.455-.409A1.192,1.192,0,0,1,0,14.618a.97.97,0,0,1,.27-.693.894.894,0,0,1,.693-.291.741.741,0,0,1,.693.27,1.815,1.815,0,0,1,.2.693c0,.381.2.575.492.575a.817.817,0,0,0,.693-.478,6.983,6.983,0,0,0,.568-1.469L6,5.543H4.5l.236-.776h1.5l.159-.54a14.548,14.548,0,0,1,.693-2.016A4.544,4.544,0,0,1,8.313.694,2.91,2.91,0,0,1,10.281,0a2.425,2.425,0,0,1,.8.145,1.5,1.5,0,0,1,.693.429.963.963,0,0,1,.236.693Z"
| transform="translate(398 948)" />
| <path class="b"
| d="M18.323,5.668a3.505,3.505,0,0,1-.152,1.046H17.36a3.969,3.969,0,0,0,.166-1.06.5.5,0,0,0-.062-.236.27.27,0,0,0-.249-.132.346.346,0,0,0-.229.076c-.069.055-.222.208-.471.471L14.936,7.489a22.329,22.329,0,0,0-1.552,1.621l-1.815,1.974a2.168,2.168,0,0,1-1.385.859c-.492,0-.741-.333-.741-.991a3.575,3.575,0,0,1,.3-1.385h.914a4.766,4.766,0,0,0-.263,1.1c0,.18.048.263.159.263s.242-.111.464-.333l2.147-2.286c-.006-.033,1.525-1.611,1.524-1.6l1.3-1.385a2.078,2.078,0,0,1,1.385-.8.755.755,0,0,1,.776.388,1.9,1.9,0,0,1,.173.776Z"
| transform="translate(398 948)" />
| <path class="a"
| d="M14.936,7.489l.693,2.251a5.154,5.154,0,0,0,.236.61c.083.159.18.242.3.242a.82.82,0,0,0,.533-.457,4.849,4.849,0,0,0,.339-.817H17.8a4.849,4.849,0,0,1-.693,1.51,2.813,2.813,0,0,1-.873.852,1.766,1.766,0,0,1-.88.27,1.178,1.178,0,0,1-1.018-.464,4.357,4.357,0,0,1-.623-1.309l-.326-1.067a6.4,6.4,0,0,0-.222-.8L12.747,7c-.083-.27-.152-.478-.2-.6a1.136,1.136,0,0,0-.194-.312.4.4,0,0,0-.284-.118c-.326,0-.6.423-.817,1.261h-.769a6.671,6.671,0,0,1,.6-1.5,3.034,3.034,0,0,1,.81-.873,1.663,1.663,0,0,1,.942-.312,1.344,1.344,0,0,1,1.067.471,3.692,3.692,0,0,1,.644,1.268l.139.436C14.672,6.7,14.936,7.489,14.936,7.489Z"
| transform="translate(398 948)" />
| </g>
| </svg>
| </span>
| </li>
| </ul>
| <div v-if="isShowExampleThree">
| <p>
| <span class="zt-ls"><b>解</b></span>（1）
| 函数<i>f</i>（<i>x</i>）=3<i>x</i><sup>2</sup>+1的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，
| </p>
| <p>而</p>
| <p class="center">
| <i>f</i>（-<i>x</i>）=3（-<i>x</i>）<sup>2</sup>+1=3<i>x</i><sup>2</sup>+1=<i>f</i>（<i>x</i>），
| </p>
| <p>
| 所以，函数<i>f</i>（<i>x</i>）=3<i>x</i><sup>2</sup>+1是偶函数.
| </p>
| </div>
| <div v-if="isShowExampleFour">
| <p>
| （2）
| 函数<i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，而
| </p>
| <p class="center">
| <i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>2</sup>+（-<i>x</i>）=<i>x</i><sup>2</sup>-<i>x</i>≠<i>f</i>（<i>x</i>），
| </p>
| <p>
| 所以，函数<i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>不是偶函数.
| </p>
| </div>
| <div v-if="isShowExampleFive">
| <p>
| （3）
| 函数<i>f</i>（<i>x</i>）=5<i>x</i>+2的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<i>R</i>，而
| </p>
| <p class="center">
| <i>f</i>（-<i>x</i>）=5（-<i>x</i>）+2=-5<i>x</i>+2≠<i>f</i>（<i>x</i>），
| </p>
| <p>所以，函数<i>f</i>（<i>x</i>）=5<i>x</i>+2不是偶函数.</p>
| </div>
| <div class="bk-hzjl">
| <div class="bj1-hzjl">
| <p class="left">
| <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
| </p>
| </div>
| <examinations :cardList="questionData[98]" sourceType="json"
| v-if="questionData" ></examinations>
| </div>
| </div>
| </div>
| </div>
| <!-- 092 -->
| <div class="page-box" page="99">
| <div v-if="showPageList.indexOf(99) > -1">
| <ul class="page-header-odd fl al-end">
| <li>092</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
| <div class="bj" >
| <examinations :cardList="questionData[99]" sourceType="json" inputBc="#d3edfa"
| v-if="questionData" ></examinations>
| <p class="gr-title">
| 四、函数 f(x)=x’-3 的图像在
| 轴左边的部分如图所示，请你画出这个函数图像在 y轴右边的部分.
| </p>
| <div>
| <!-- <paint
| :page="99"
| :imgUrl="
| this.config.activeBook.resourceUrl + '/images/0103-2.jpg'
| "
| /> -->
| <graffiti
| :page="99"
| :bcImg="this.config.activeBook.resourceUrl + '/images/0103-2.jpg'"
| :imgWidth="520"
| :imgHeight="494"
| />
| </div>
| </div>
| </div>
| </div>
| </div>
| <!-- 093 -->
| <div class="page-box" page="100">
| <div v-if="showPageList.indexOf(100) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>093</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/wttc.jpg" /></p>
| <p>函数<i>f</i>（<i>x</i>）=2<i>x</i>和<i>g</i>（<i>x</i>）=<i>x</i><sup>3</sup>的图像有何对称性呢？</p>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/tjfx.jpg" /></p>
| <p>列出表3-13和表3-14，画出函数<i>f</i>（<i>x</i>）=2<i>x</i>和<i>g</i>（<i>x</i>）=<i>x</i><sup>3</sup>的图像，如图3-19所示.</p>
| <p class="img">表3-13</p>
| <p class="center"><img class="img-a" alt="" src="../../assets/images/0104-1.jpg" /></p>
| <p class="img">表3-14</p>
| <p class="center"><img class="img-a" alt="" src="../../assets/images/0104-2.jpg" /></p>
| <p class="center"><img class="img-b" alt="" src="../../assets/images/0104-3.jpg" /></p>
| <p class="img">图3-19</p>
| <p>图3-19（1）
| 中，函数<i>f</i>（<i>x</i>）=2<i>x</i>的定义域是（-∞，+∞），函数图像关于原点中心对称.表3-13中，当自变量取一对相反数时，对应的函数值是一对相反数，如<i>f</i>（-1）=-2=-<i>f</i>（1），<i>f</i>（-2）=-4=-<i>f</i>（2），<i>f</i>（-3）=-6=-<i>f</i>（3），…实际上，对任意<i>x</i>∈（-∞，+∞），都有<i>f</i>（-<i>x</i>）=2×（-<i>x</i>）=-2<i>x</i>=-<i>f</i>（<i>x</i>），即<i>f</i>（-<i>x</i>）=-<i>f</i>（<i>x</i>）.
| </p>
| <p>图3-19（2）
| 中，函数<i>g</i>（<i>x</i>）=<i>x</i><sup>3</sup>的定义域是（-∞，+∞），函数图像也关于原点中心对称.表3-14中，当自变量取一对相反数时，对应的函数值也是一对相反数，如
| </p>
| </div>
| </div>
| </div>
| <!-- 094 -->
| <div class="page-box" page="101">
| <div v-if="showPageList.indexOf(101) > -1">
| <ul class="page-header-odd fl al-end">
| <li>094</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <p class="t0">
| <i>g</i>（-1）=-1=-<i>g</i>（1），<i>g</i>（-2）=-8=-<i>g</i>（2），<i>g</i>（-3）=-27=-<i>g</i>（3），…实际上，对任意<i>x</i>∈（-∞，+∞），都有<i>g</i>（-<i>x</i>）=（-<i>x</i>）<sup>3</sup>=-<i>x</i><sup>3</sup>=-<i>g</i>（<i>x</i>），即<i>g</i>（-<i>x</i>）=-<i>g</i>（<i>x</i>）.
| </p>
| <p>这两个函数的图像分别关于原点中心对称；当自变量取定义域中任意一对相反数时，对应的函数值也是一对相反数，这种函数就是奇函数.</p>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" /></p>
| <p>一般地，设函数<i>f</i>（<i>x</i>）的定义域为<i>D</i>，如果对于<span class="u">任意</span><i>x</i>∈<i>D</i>，<span
| class="u">都有</span>-<i>x</i>∈<i>D</i>，且<i>f</i>（-<i>x</i>）=-<i>f</i>（<i>x</i>），那么函数<i>f</i>（<i>x</i>）就叫作<b>奇函数</b>，如图3-20所示.<b>奇函数的图像关于原点中心对称</b>.
| </p>
| <p>我们也可以由函数图像是否关于原点中心对称来判断函数是不是奇函数.</p>
| <p class="center"><img class="img-f" alt="" src="../../assets/images/0105-1.jpg" /></p>
| <p class="img">图3-20</p>
| <p class="p-btn" >
| <span>
| <span class="zt-ls"><b>例4</b></span> 根据图3-21中函数的图像，判断哪些函数是奇函数.
| </span>
| <span class="btn-box" @click="isShowAnswer24 = !isShowAnswer24">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <p class="center"><img class="img-b" alt="" src="../../assets/images/0105-2.jpg" /></p>
| <p class="img">图3-21</p>
| <p v-if="isShowAnswer24" ><span class="zt-ls"><b>解</b></span> 在四个函数图像中，图3-21（1） 、图3-21（2） 和图3-21（3） 的函数图像关于原点中心对称；图3-21（4）
| 的函数图像不是关于原点中心对称的.根据奇函数的图像具有关于原点中心对称的特点，图3-21（1） 、图3-21（2） 和图3-21（3） 的函数是奇函数，图3-21（4） 的函数不是奇函数.</p>
| </div>
| </div>
| </div>
| <!-- 095 -->
| <div class="page-box" page="102">
| <div v-if="showPageList.indexOf(102) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>095</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <p class="p-btn" >
| <span>
| <span class="zt-ls"><b>例5</b></span> 已知函数<math display="0">
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <mfrac>
| <mn>1</mn>
| <mi>x</mi>
| </mfrac>
| </math>图像在<i>y</i>轴右边的部分如图3-22所示.试画出这个函数图像在<i>y</i>轴左边的部分.
| </span>
| <span class="btn-box" @click="isShowAnswer25 = !isShowAnswer25">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <p class="center"><img class="img-c" alt="" src="../../assets/images/0106-3.jpg" /></p>
| <p class="img">图3-22</p>
| <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
| <div v-if="isShowAnswer25" >
| <p><span class="zt-ls"><b>解</b></span> 函数<math display="0">
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <mfrac>
| <mn>1</mn>
| <mi>x</mi>
| </mfrac>
| </math>的定义域是（-∞，0）∪（0+∞），因为它是奇函数，所以根据其图像关于原点中心对称的特点，即可画出这个函数在<i>x</i>∈（-∞，0）上的图像.</p>
| <p>
| 如图3-23所示，在<i>y</i>轴右边的图像上取三个不同点<i>A</i>，<i>B</i>和<i>C</i>，并画出它们分别关于原点对称的点<i>A</i>′，<i>B</i>′和<i>C</i>′，然后按相同方式用光滑的曲线连线，就得到这个函数的图像在<i>y</i>轴左边的部分.
| </p>
| <p class="center"><img class="img-c" alt="" src="../../assets/images/0106-4.jpg" /></p>
| <p class="img">图3-23</p>
| <p>与偶函数的判定方法类似，除了借助函数的图像来判断函数是不是奇函数，也可用定义判断函数是不是奇函数.</p>
| </div>
| <p><span class="zt-ls"><b>例6</b></span> 判断下列函数是不是奇函数.</p>
| <p class="p-btn" >
| <span>（1） <i>f</i>（<i>x</i>）=<i>x</i><sup>3</sup>+<i>x</i>；</span>
| <span class="btn-box" @click="isShowAnswer26 = !isShowAnswer26">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer26" >
| <p><span class="zt-ls"><b>解</b></span>（1）
| 函数<i>f</i>（<i>x</i>）=<i>x</i><sup>3</sup>+<i>x</i>的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，且
| </p>
| <p class="center">
| <i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>3</sup>+（-<i>x</i>）=-<i>x</i><sup>3</sup>-<i>x</i>=-（<i>x</i><sup>3</sup>+<i>x</i>）=-<i>f</i>（<i>x</i>）.
| </p>
| <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i><sup>3</sup>+<i>x</i>是奇函数.</p>
| </div>
| <p class="p-btn" >
| <span>
| （2） <math display="0">
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <mi>x</mi>
| <mo>+</mo>
| <mfrac>
| <mn>1</mn>
| <mi>x</mi>
| </mfrac>
| </math>；
| </span>
| <span class="btn-box" @click="isShowAnswer27 = !isShowAnswer27">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer27" >
| <p>
| <span class="zt-ls"><b>解</b></span>（2）
| 要使函数<i>f</i>（<i>x</i>）有意义，必须满足<i>x</i>≠0，所以函数<i>f</i>（<i>x</i>）的定义域是<i>D</i>={<i>x</i>|<i>x</i>≠0}，对任意<i>x</i>∈<i>D</i>，都有-<i>x</i>∈<i>D</i>，且
| </p>
| <math display="block">
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mo>−</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <mo>−</mo>
| <mi>x</mi>
| <mo>+</mo>
| <mfrac>
| <mn>1</mn>
| <mrow>
| <mo>−</mo>
| <mi>x</mi>
| </mrow>
| </mfrac>
| <mo>=</mo>
| <mo>−</mo>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo>+</mo>
| <mfrac>
| <mn>1</mn>
| <mi>x</mi>
| </mfrac>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <mo>−</mo>
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>.</mo>
| </math>
| <p>所以，函数<math display="0">
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <mo>−</mo>
| <mi>x</mi>
| <mo>+</mo>
| <mfrac>
| <mn>1</mn>
| <mi>x</mi>
| </mfrac>
| </math>是奇函数.
| </p>
| </div>
| <p class="p-btn" >
| <span>（3） <i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|.</span>
| <span class="btn-box" @click="isShowAnswer28 = !isShowAnswer28">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer28" >
| <p > <span class="zt-ls"><b>解</b></span>（3） 函数<i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，但是</p>
| <p class="center">
| <i>f</i>（-<i>x</i>）=（-<i>x</i>）+|-<i>x</i>|=-<i>x</i>+|<i>x</i>|=-（<i>x</i>-|<i>x</i>|）≠-<i>f</i>（<i>x</i>）.
| </p>
| <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|不是奇函数.</p>
| </div>
| </div>
| </div>
| </div>
| <!-- 096 -->
| <div class="page-box" page="103">
| <div v-if="showPageList.indexOf(103) > -1">
| <ul class="page-header-odd fl al-end">
| <li>096</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <div class="bk-hzjl">
| <div class="bj1-hzjl">
| <p class="left">
| <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
| </p>
| </div>
| <examinations :cardList="questionData[103] ? questionData[103][1] : []" sourceType="json" v-if="questionData">
| </examinations>
| </div>
| <p>如果一个函数是奇函数或偶函数，那么就称这个函数具有<b>奇偶性</b>.否则，函数不具有奇偶性.</p>
| <p><span class="zt-ls"><b>例7</b></span> 判断下列函数的奇偶性.</p>
| <p class="p-btn" >
| <span>（1） <i>f</i>（<i>x</i>）=<i>x</i><sup>4</sup>；</span>
| <span class="btn-box" @click="isShowAnswer29 = !isShowAnswer29">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer29" >
| <p><span class="zt-ls"><b>解</b></span>（1）
| <i>f</i>（<i>x</i>）的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，且
| </p>
| <p class="center"><i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>4</sup>=<i>x</i><sup>4</sup>=<i>f</i>（<i>x</i>），</p>
| <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i><sup>4</sup>是偶函数.</p>
| </div>
| <p class="p-btn">
| <span>
| （2） <math display="0">
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <mo>−</mo>
| <mi>x</mi>
| <mo>−</mo>
| <mfrac>
| <mn>1</mn>
| <mi>x</mi>
| </mfrac>
| </math>；
| </span>
| <span class="btn-box" @click="isShowAnswer30 = !isShowAnswer30">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer30" >
| <p>
| <span class="zt-ls"><b>解</b></span>（2）
| 要使函数<i>f</i>（<i>x</i>）有意义，必须满足<i>x</i>≠0，所以函数<i>f</i>（<i>x</i>）的定义域是<i>D</i>={<i>x</i>|<i>x</i>≠0}，对任意<i>x</i>∈<i>D</i>，都有-<i>x</i>∈<i>D</i>，
| 且</p>
| <math display="block">
| <mi>f</mi>
| <mo stretchy="false">(</mo>
| <mo>−</mo>
| <mi>x</mi>
| <mo stretchy="false">)</mo>
| <mo>=</mo>
| <mo>−</mo>
| <mi>x</mi>
| <mo>−</mo>
| <mfrac>
| <mn>1</mn>
| <mrow>
| <mo>−</mo>
| <mi>x</mi>
| </mrow>
| </mfrac>
| <mo>=</mo>
| <mo>−</mo>
| <mi>x</mi>
| <mo>+</mo>
| <mfrac>
| <mn>1</mn>
| <mi>x</mi>
| </mfrac>
| <mo>=</mo>
| <mo>−</mo>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo>−</mo>
| <mfrac>
| <mn>1</mn>
| <mi>x</mi>
| </mfrac>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <mo>−</mo>
| <mi>f</mi>
| <mo stretchy="false">(</mo>
| <mi>x</mi>
| <mo stretchy="false">)</mo>
| <mo>,</mo>
| </math>
| <p>所以，函数<math display="0">
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <mi>x</mi>
| <mo>−</mo>
| <mfrac>
| <mn>1</mn>
| <mi>x</mi>
| </mfrac>
| </math>是奇函数.
| </p>
| </div>
| <p class="p-btn">
| <span>
| （3） <i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>；
| </span>
| <span class="btn-box" @click="isShowAnswer31 = !isShowAnswer31">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer31" >
| <p> <span class="zt-ls"><b>解</b></span>（3）
| 函数<i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，且
| </p>
| <p class="center"><i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>2</sup>+（-<i>x</i>）=<i>x</i><sup>2</sup>-<i>x</i>，</p>
| <p>但 <i>f</i>（-<i>x</i>）≠<i>f</i>（<i>x</i>），且<i>f</i>（-<i>x</i>）≠-<i>f</i>（<i>x</i>），</p>
| <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>既不是奇函数，也不是偶函数.</p>
| </div>
| <p class="p-btn" >
| <span>
| （4）<math display="0">
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <mfrac>
| <mn>1</mn>
| <mrow>
| <mi>x</mi>
| <mo>−</mo>
| <mn>1</mn>
| </mrow>
| </mfrac>
| </math>.
| </span>
| <span class="btn-box" @click="isShowAnswer32 = !isShowAnswer32">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer32" >
| <p> <span class="zt-ls"><b>解</b></span>（4）
| 要使函数<i>f</i>（<i>x</i>）有意义，必须满足<i>x</i>-1≠0，所以函数<i>f</i>（<i>x</i>）的定义域是<i>D</i>={<i>x</i>|<i>x</i>≠1}，对任意<i>x</i>∈<i>D</i>，不都有-<i>x</i>∈<i>D</i>成立.
| </p>
| <p>所以，函数<math display="0">
| <mi>f</mi>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>x</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| <mo>=</mo>
| <mfrac>
| <mn>1</mn>
| <mrow>
| <mi>x</mi>
| <mo>−</mo>
| <mn>1</mn>
| </mrow>
| </mfrac>
| </math>不具有奇偶性，它既不是奇函数也不是偶函数.
| </p>
| </div>
| <div class="bk-hzjl">
| <div class="bj1-hzjl">
| <p class="left"><img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" /></p>
| </div>
| <examinations :cardList="questionData[103] ? questionData[103][2] : []" sourceType="json"
| v-if="questionData" ></examinations>
| </div>
| </div>
| </div>
| </div>
| <!-- 097 -->
| <div class="page-box" page="104">
| <div v-if="showPageList.indexOf(104) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>097</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
| <div class="bj">
| <examinations :cardList="questionData[104]" sourceType="json"
| v-if="questionData" ></examinations>
| </div>
|
| </div>
| </div>
| </div>
| <!-- 098 -->
| <div class="page-box hidePage" page="105">
| </div>
| <!-- 099 -->
| <div class="page-box" page="106">
| <div v-if="showPageList.indexOf(106) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>098-099</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <h3 id="c032">习题3.3<span class="fontsz2">＞＞＞</span></h3>
| <div class="bj" >
| <examinations :cardList="questionData[105]" sourceType="json"
| v-if="questionData" ></examinations>
| </div>
| <h2 id="b018">3.4 函数的应用<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/tjfx.jpg" /></p>
| <p>
| 函数是刻画变量之间对应关系的数学模型和工具，在社会生活、生产中，函数关系随处可见，函数的应用也非常广泛.例如，物体运动的路程是时间的函数，购买物品费用是物品数量的函数，圆的面积是半径的函数，居民生活用水（电、燃气）费用是用水（电、燃气）量的函数等.
| </p>
| </div>
| </div>
| </div>
| <!-- 100 -->
| <div class="page-box" page="107">
| <div v-if="showPageList.indexOf(107) > -1">
| <ul class="page-header-odd fl al-end">
| <li>100</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <p>
| <span>
| <span class="zt-ls">
| <b>例1</b></span> 住在A城的小李早晨8：00出发，驾驶小轿车从A城以80 km/h 的速度到200 km处的B城，他在B城停留了3 h 后，再以100
| km/h的速度返回A城.在不考虑堵车等其他因素的情况下，设小李从A城出发<i>x</i>（h）后，小李与A城的距离是<i>y</i>（km）.
| </span>
| <span class="btn-box" @click="openDialog(thinkFive)">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
| <path class="a"
| d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
| transform="translate(-3761 14334.001)" />
| </svg>
| </span>
| </p>
| <p class="p-btn" >
| <span>
| （1） 用解析法表示函数<i>y</i>=<i>f</i>（<i>x</i>）；
| </span>
| <span class="btn-box" @click="isShowAnswer33 = !isShowAnswer33">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer33" >
| <p><span class="zt-ls"><b>解</b></span>（1） 小李从A城出发到B 城用时<math display="0">
| <mfrac>
| <mn>200</mn>
| <mn>80</mn>
| </mfrac>
| <mo>=</mo>
| <mn>2.5</mn>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>h</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| </math>，<i>x</i>的取值范围是{<i>x</i>|0＜<i>x</i>≤2.5}，<i>y</i>与<i>x</i>的对应关系是<i>y</i>=80<i>x</i>；</p>
| <p>小李到B城后停留3 h，x的取值范围是{<i>x</i>|2.5＜<i>x</i>≤5.5}，对应关系是<i>y</i>=200；</p>
| <p>小李从<i>B</i>城返回<i>A</i>城用时<math display="0">
| <mfrac>
| <mn>200</mn>
| <mn>100</mn>
| </mfrac>
| <mo>=</mo>
| <mn>2</mn>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">(</mo>
| <mi>h</mi>
| <mo data-mjx-texclass="CLOSE">)</mo>
| </mrow>
| </math>，<i>x</i>的取值范围是{<i>x</i>|5.5＜<i>x</i>≤7.5}，<i>y</i>与<i>x</i>的对应关系是<i>y</i>=200-100（<i>x</i>-5.5），即<i>y</i>=-100<i>x</i>+750.
| </p>
| <p>因此，用解析法将函数<i>f</i>（<i>x</i>）表示为<math display="0">
| <mi>y</mi>
| <mo>=</mo>
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">{</mo>
| <mtable columnalign="left left" columnspacing="1em" rowspacing="4pt">
| <mtr>
| <mtd>
| <mn>80</mn>
| <mi>x</mi>
| <mo>,</mo>
| </mtd>
| <mtd>
| <mn>0</mn>
| <mo><</mo>
| <mi>x</mi>
| <mo>⩽</mo>
| <mn>2.5</mn>
| </mtd>
| </mtr>
| <mtr>
| <mtd>
| <mn>200</mn>
| <mo>,</mo>
| </mtd>
| <mtd>
| <mn>2.5</mn>
| <mo><</mo>
| <mi>x</mi>
| <mo>⩽</mo>
| <mn>5.5</mn>
| <mo>,</mo>
| </mtd>
| </mtr>
| <mtr>
| <mtd>
| <mo>−</mo>
| <mn>100</mn>
| <mi>x</mi>
| <mo>+</mo>
| <mn>750</mn>
| <mo>,</mo>
| <mn>5.5</mn>
| <mo><</mo>
| <mi>x</mi>
| <mo>⩽</mo>
| <mn>7.5</mn>
| </mtd>
| </mtr>
| </mtable>
| <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
| </mrow>
| </math>.
| </p>
| </div>
| <p class="p-btn" >
| <span>（2） 画出函数<i>y</i>=<i>f</i>（<i>x</i>）的图像；</span>
| <span class="btn-box" @click="isShowAnswer34 = !isShowAnswer34">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer34">
| <p> <span class="zt-ls"><b>解</b></span>（2） 函数<i>y</i>=<i>f</i>（<i>x</i>）的图像如图3-24所示.</p>
| <p class="center"><img class="img-f" alt="" src="../../assets/images/0111-4.jpg" /></p>
| <p class="img">图3-24</p>
| </div>
| <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
| <p class="p-btn" >
| <span>（3） 小李在返回A城途中，15：00刚好接到家人的电话，这时他距离A城多少千米？</span>
| <span class="btn-box" @click="isShowAnswer35 = !isShowAnswer35">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer35" >
| <p> <span class="zt-ls"><b>解</b></span>（3） 小李从早晨8：00出发到15：00，共经过了7h，所以<i>x</i>=7，由（1） 中解析式得小李与<i>A</i>城的距离为</p>
| <p class="center">-100×7+750=50（km）.</p>
| <p>所以，小李返回A城途中接到家人电话时，距离A城刚好50 km.</p>
| </div>
| </div>
| </div>
| </div>
| <!-- 101 -->
| <div class="page-box" page="108">
| <div v-if="showPageList.indexOf(108) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>101</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <p class="p-btn" >
| <span>
| <span class="zt-ls"><b>例2</b></span> 某农户要用6 000块砖建造三间面积相等的饲养室，如图3-25所示，其中<i>AB</i>，<i>AD</i>两面靠墙，每修筑长度1
| m的新墙需要砖200块.当<i>AB</i>为多少米时，修建的三间饲养室的总面积最大？最大面积是多少？
| </span>
| <span class="btn-box" @click="openDialog(thinkSix)">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
| <path class="a"
| d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
| transform="translate(-3761 14334.001)" />
| </svg>
| </span>
| <span class="btn-box" @click="isShowAnswer36 = !isShowAnswer36">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <p class="center"><img class="img-f" alt="" src="../../assets/images/0112-1.jpg" /></p>
| <p class="img">图3-25</p>
| <div v-if="isShowAnswer36" >
| <p><span class="zt-ls"><b>解</b></span> 因为每修筑长度1 m的新墙需要砖200块，所以6 000块砖可以修筑新墙的总长度是6
| 000÷200=30（m）.设<i>AB</i>为<i>x</i>（m），则<i>BC</i>为（30-3<i>x</i>）（m），三间饲养室的总面积为<i>y</i>（m<sup>2</sup>）.</p>
| <p>于是<i>y</i>=（30-3<i>x</i>）<i>x</i>，要有实际意义，必须满足<math display="0">
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">{</mo>
| <mtable columnspacing="1em" rowspacing="4pt">
| <mtr>
| <mtd>
| <mi>x</mi>
| <mo>＞</mo>
| <mn>0</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| </mtr>
| <mtr>
| <mtd>
| <mn>30</mn>
| <mo>−</mo>
| <mn>3</mn>
| <mi>x</mi>
| <mo>＞</mo>
| <mn>0</mn>
| </mtd>
| <mtd></mtd>
| </mtr>
| </mtable>
| <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
| </mrow>
| </math>.</p>
| <p>所以，<i>y</i>与<i>x</i>的函数关系是<i>y</i>=-3<i>x</i><sup>2</sup>+30<i>x</i>，0＜<i>x</i>＜10.</p>
| <p>整理得<i>y</i>=-3（<i>x</i>-5）<sup>2</sup>+75.</p>
| <p>所以，当<i>x</i>=5时，<i>y</i>值最大，最大值为75.</p>
| <p>即当<i>AB</i>为5 m时，三间饲养室的总面积最大，最大面积是75 m<sup>2</sup>.</p>
| <p>在实际生活中，很多与二次函数有关的最值问题都可通过分析、研究后，建立相应二次函数的数学模型，并运用二次函数的图像性质求最值.</p>
| </div>
| <p class="p-btn" >
| <span>
| <span class="zt-ls"><b>例3</b></span> 某批发商购入一批30元/kg的绿色食品，若以40元/kg销售，则每月可批发销售400
| kg.由批发销售经验知道，每月销售量<i>y</i>（kg
| ）是销售单价<i>x</i>（元）的一次函数，其图像如图3-26所示.
| </span>
| <span class="btn-box" @click="openDialog(thinkSeven)">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
| <path class="a"
| d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
| transform="translate(-3761 14334.001)" />
| </svg>
| </span>
| </p>
| <p class="center"><img class="img-c" alt="" src="../../assets/images/0112-3.jpg" /></p>
| <p class="img"> 图3-26</p>
| <p class="p-btn">
| <span>（1） 用解析法表示函数<i>y</i>=<i>f</i>（<i>x</i>）；</span>
| <span class="btn-box" @click="isShowAnswer38 = !isShowAnswer38">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer38" >
| <p><span class="zt-ls"><b>解</b></span>（1） 设函数<i>y</i>=<i>f</i>（<i>x</i>）的解析式是<i>y</i>=<i>kx</i>+<i>b</i>，则</p>
| <p><math display="0">
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">{</mo>
| <mtable columnspacing="1em" rowspacing="4pt">
| <mtr>
| <mtd>
| <mn>40</mn>
| <mi>k</mi>
| <mo>+</mo>
| <mi>b</mi>
| <mo>=</mo>
| <mn>400</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| </mtr>
| <mtr>
| <mtd>
| <mn>50</mn>
| <mi>k</mi>
| <mo>+</mo>
| <mi>b</mi>
| <mo>=</mo>
| <mn>200</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| </mtr>
| </mtable>
| <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
| </mrow>
| </math>，解得<math display="0">
| <mrow data-mjx-texclass="INNER">
| <mo data-mjx-texclass="OPEN">{</mo>
| <mtable columnspacing="1em" rowspacing="4pt">
| <mtr>
| <mtd>
| <mi>k</mi>
| <mo>=</mo>
| <mo>−</mo>
| <mn>20</mn>
| <mo>，</mo>
| </mtd>
| <mtd></mtd>
| </mtr>
| <mtr>
| <mtd>
| <mi>b</mi>
| <mo>=</mo>
| <mn>1200.</mn>
| </mtd>
| <mtd></mtd>
| </mtr>
| </mtable>
| <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
| </mrow>
| </math></p>
| <p>即<i>y</i>=-20<i>x</i>+1 200.</p>
| <p>根据题意，当30≤<i>x</i>≤60时，函数<i>y</i>=-20<i>x</i>+1 200才有实际意义.</p>
| <p>所以，函数<i>y</i>=<i>f</i>（<i>x</i>）的解析式可表示为</p>
| <p class="center"><i>y</i>=-20<i>x</i>+1 200，30≤<i>x</i>≤60.</p>
| </div>
| <p class="p-btn">
| <span>
| （2） 该批发商不低于购入价进行销售，设该批发商每月销售这批绿色食品可获得利润为<i>w</i>元，用解析法表示函数<i>w</i>=<i>g</i>（<i>x</i>）；
| </span>
| <span class="btn-box" @click="isShowAnswer39 = !isShowAnswer39">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer39" >
| <p> <span class="zt-ls"><b>解</b></span>（2） 由题意得，<i>w</i>=（<i>x</i>-30）<i>y</i></p>
| <p> =（<i>x</i>-30）（-20<i>x</i>+1 200）</p>
| <p> =-20<i>x</i><sup>2</sup>+1 800<i>x</i>-36 000，</p>
| <p>所以，函数<i>w</i>=<i>g</i>（<i>x</i>）的解析式可表示为</p>
| <p class="center"><i>w</i>=-20<i>x</i><sup>2</sup>+1 800<i>x</i>-36 000，30≤<i>x</i>≤60.</p>
| </div>
| <p class="p-btn">
| <span>
| （3） 当销售单价为多少时，该批发商每月可获得最大利润？最大利润是多少？
| </span>
| <span class="btn-box" @click="isShowAnswer40 = !isShowAnswer40">
| <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
| <path class="a"
| d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
| transform="translate(-3327.144 15329)" />
| </svg>
| </span>
| </p>
| <div v-if="isShowAnswer40" >
| <p> <span class="zt-ls"><b>解</b></span>（3） 由（2） 知，<i>w</i>=-20<i>x</i><sup>2</sup>+1 800<i>x</i>-36 000，30≤<i>x</i>≤60，配方得</p>
| <p class="center"><i>w</i>=-20（<i>x</i>-45）<sup>2</sup>+4 500.</p>
| <p>所以，当<i>x</i>=45时，<i>w</i>的值最大，最大值是4 500.</p>
| <p>答：当销售单价为45元时，该批发商每月可获得最大利润，最大利润是4 500元.</p>
| </div>
| </div>
| </div>
| </div>
| <!-- 102 -->
| <div class="page-box" page="109">
| <div v-if="showPageList.indexOf(109) > -1">
| <ul class="page-header-odd fl al-end">
| <li>102-103</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
| <div class="bj">
| <examinations :cardList="questionData[110]" sourceType="json"
| v-if="questionData" ></examinations>
| </div>
| </div>
| </div>
| </div>
| <!-- 103 -->
| <div class="page-box hidePage" page="110">
| </div>
| <!-- 104 -->
| <div class="page-box" page="111">
| <div v-if="showPageList.indexOf(111) > -1">
| <ul class="page-header-odd fl al-end">
| <li>104-106</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <h3 id="c033">习题3.4<span class="fontsz2">＞＞＞</span></h3>
| <div class="bj">
| <examinations :cardList="questionData[111]" sourceType="json" inputBc="#d3edfa"
| v-if="questionData" ></examinations>
| </div>
| </div>
| </div>
| </div>
|
| <!-- 105 -->
| <div class="page-box hidePage" page="112">
| </div>
| <!-- 106 -->
| <div class="page-box hidePage" page="113">
| </div>
| <!-- 107 -->
| <div class="page-box" page="114">
| <div v-if="showPageList.indexOf(114) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>107</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <h2 id="b019">数学园地<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
| <p class="center">函数概念及符号的形成与发展</p>
| <p>我们已经系统学习了函数的概念、表示方法、性质等，现在我们一起来了解函数概念的形成与发展过程.</p>
| <p>17世纪，意大利科学家伽利略在《关于两门新科学的对话》一书中，提出了函数或变量关系的概念，借助文字和比例关系表达函数的关系.法国数学家笛卡儿在他的解析几何中注意到了一个变量对于另一个变量的依赖关系.</p>
| <p>1673年，德国数学家莱布尼茨首次使用“函数”表示“幂”，同时牛顿在微积分的讨论中，使用“流量”来表示变量间的关系，这时的函数概念还较为模糊.</p>
| <p>
| 1718年，瑞士数学家伯努利在莱布尼茨函数概念的基础上，从解析的角度提出了函数的概念：“由变量<i>x</i>和常数所构成的式子叫作<i>x</i>的函数”，记作<i>Χ</i>或ξ，后来他又改用<i>Φx</i>表示<i>x</i>的函数.
| </p>
| <p>1734 年，瑞士数学家欧拉以<i>f</i>（）
| 表示函数，这是数学史上函数首次以“<i>f</i>”符号表示！他把函数定义为“如果某些变量，以某一种方式依赖于另一些变量，即当后面这些变量变化时，前面这些变量也随之变化，我们把前面的变量称为后面变量的函数.”并采用大写希腊字母<i>Πx</i>，<i>Φx</i>及<i>Δx</i>表示<i>x</i>的函数.
| </p>
| <p>1797年，法国数学家拉格朗日大力推动以<i>f</i>，<i>F</i>，<i>Φ</i>及<i>y</i>表示函数，并且沿用至今！</p>
| <p>1821年，法国数学家柯西给出函数的定义：“在某些变数间存在着一定的关系，当一经给定其中某一变数的值，其他变数的值可随之而确定时，则将最初的变数叫自变量，其他各变数叫函数.”</p>
| <p>1822年，法国数学家傅立叶发现某些函数可用曲线表示，也可以用一个式子表示，或用多个式子表示，他把对函数的认识又推进到了一个新的层次.</p>
| <p>1893年，意大利数学家皮亚诺开始采用符号<i>y</i>=<i>f</i>（<i>x</i>）表示函数，这就是我们今天见到的函数符号！</p>
| <p>
| 后来，数学家们用“集合”和“对应”给出了近代函数的概念，把函数的对应关系、定义域及值域进一步具体化：“若对集合<i>M</i>的任意元素<i>x</i>，总有集合<i>N</i>中确定的元素<i>y</i>与之对应，则称在集合<i>M</i>上定义一个函数，记为<i>y</i>=<i>f</i>（<i>x</i>）.”
| </p>
| </div>
| </div>
| </div>
| <!-- 108 -->
| <div class="page-box" page="115">
| <div v-if="showPageList.indexOf(115) > -1">
| <ul class="page-header-odd fl al-end">
| <li>108</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <h2 id="b020">单元小结<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
| <p class="bj2"><b>学习导图</b></p>
| <p class="center"><img class="img-b" alt="" src="../../assets/images/0119-1.jpg" /></p>
| <p class="bj2"><b>学习指导</b></p>
| <p>1.函数的概念.</p>
| <p>（1） 函数的定义：一般地， 设<i>A</i>，<i>B</i>是非空数集， 如果存在一个对应关系<i>f</i>，使对于集合 <i>A</i> 中的每一个数<i>x</i>，在集合<i>B</i>
| 中都有唯一确定的数<i>y</i>
| 和它对应，那么就把对应关系<i>f</i>称为定义在集合<i>A</i>上的一个<b>函数</b>，记作<i>y</i>=<i>f</i>（<i>x</i>），<i>x</i>∈<i>A</i>.其中，<i>x</i>叫作自变量，<i>x</i>的取值范围<i>A</i>叫作函数的<b>定义域</b>；与<i>x</i>的值相对应的<i>y</i>值叫作函数值，函数值的集合{<i>f</i>（<i>x</i>）｜<i>x</i>∈<i>A</i>}叫作函数的<b>值域</b>.
| </p>
| <p>定义域和对应关系是函数的两个要素，值域是由定义域与函数关系所决定的.</p>
| <p>（2） 求函数定义域时，首先要考虑问题的实际意义.</p>
| <p>2.函数的表示方法.</p>
| <p>（1） 函数有三种表示方法：列表法、图像法和解析法.在解决问题时，应根据需要选择恰当的表示方法.</p>
| <p>（2） 分段函数：分段函数是在自变量不同的取值范围内，采用不同的对应关系的一种函数，分段函数仍然是一个函数.</p>
| <p>3.函数的单调性和奇偶性.</p>
| <p>函数的单调性和奇偶性是函数的两个基本性质.</p>
| <p>（1） 函数的单调性反映了函数值变化的趋势.单调性是相对于函数定义域的某个区间（区间是定义域的子集）而言的，所以研究函数的单调性时，必须指明单调</p>
| </div>
| </div>
| </div>
| <!-- 109 -->
| <div class="page-box" page="116">
| <div v-if="showPageList.indexOf(116) > -1">
| <ul class="page-header-box">
| <li>
| <p>第三单元 函数</p>
| </li>
| <li>
| <p><span>109</span></p>
| </li>
| </ul>
| <div class="padding-116">
| <p class="t0">区间.</p>
| <p>（2）
| 函数的奇偶性反映函数图像的对称性.奇函数、偶函数的定义域一定是关于原点对称的.若函数图像关于<i>y</i>轴对称，则该函数是偶函数；若函数图像关于原点对称，则该函数是奇函数.反之，偶函数一定关于<i>y</i>轴对称；奇函数一定关于原点对称.
| </p>
| <p>4.函数的实际应用.</p>
| <p>函数的实际应用问题主要抓住以下几个步骤：一是读懂题意；二是正确建立函数关系（分段函数、二次函数等）；三是转化为函数问题；四是做好最后的解答.</p>
| </div>
| </div>
| </div>
| <!-- 110 -->
| <div class="page-box" page="117">
| <div v-if="showPageList.indexOf(117) > -1">
| <ul class="page-header-odd fl al-end">
| <li>110-112</li>
| <li>数学.基础模块</li>
| <li>上册</li>
| </ul>
| <div class="padding-116">
| <h2 id="b021">单元检测<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
| <div class="bj" >
| <examinations :cardList="questionData[117]" sourceType="json"
| v-if="questionData" ></examinations>
| </div>
| </div>
| </div>
| </div>
| <!-- 111 -->
| <div class="page-box hidePage" page="118">
| </div>
| <!-- 112 -->
| <div class="page-box hidePage" page="119">
| </div>
| <!-- 函数控件弹窗 -->
| <el-dialog :visible.sync="dialogVisible" width="60%" :append-to-body="true" :show-close="false">
| <div slot="title" style="padding: 0 0 15px 0;position: relative;">
| <svg style="position: absolute; right:10px;cursor: pointer;" @click="dialogVisible = false" t="1718596022986"
| class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
| height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
| <path
| d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
| fill="#979797" p-id="4253"></path>
| <path
| d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
| fill="#979797" p-id="4254"></path>
| </svg>
| </div>
| <iframe src="https://www.geogebra.org/calculator" frameborder="0" style="width: 100%; min-height: 800px"></iframe>
| </el-dialog>
| <!-- 解题思路弹窗 -->
| <el-dialog :visible.sync="thinkingDialog" width="40%" :append-to-body="true" :show-close="false"
| @close="closeDialog" class="thinkDialog">
| <div slot="title" class="think-header"
| style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
| <span style=""> 分析 </span>
| <svg style="position: absolute; right:10px;cursor: pointer;" @click="thinkingDialog = false" t="1718596022986"
| class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
| height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
| <path
| d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
| fill="#979797" p-id="4253"></path>
| <path
| d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
| fill="#979797" p-id="4254"></path>
| </svg>
| </div>
| <ul>
| <li v-for="(item, index) in thinkData" :key="index">
| <div v-if="index <= showIndex" style="display: flex">
| <span style="position: relative">
| <span style="position: absolute; top: 16px; left: 13px; color: #fff">{{ index + 1 }}</span>
| <img src="../../assets/images/icon/blue-group.png" alt="" style="margin-right: 10px"
| v-if="index < thinkOne.length - 1" />
| <img src="../../assets/images/icon/blue.png" alt="" v-if="index == thinkOne.length - 1"
| style="margin-right: 10px" />
| </span>
| <p class="txt-p" v-html="item"></p>
| </div>
| </li>
| </ul>
| <div @click="changeNext" style="
| display: flex;
| flex-direction: column;
| align-items: center;
| justify-content: center;
| ">
| <img src="../../assets/images/icon/mouse.png" alt="" v-if="showIndex < thinkData.length - 1" />
| <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" t="1710234570135"
| class="icon" viewBox="0 0 1024 1024" version="1.1" p-id="5067" width="15" height="15">
| <path
| d="M2.257993 493.371555 415.470783 906.584344 512 1003.113561 608.529217 906.584344 1021.742007 493.371555 925.212789 396.842337 512 810.055127 98.787211 396.842337Z"
| fill="#1296db" p-id="5068" />
| <path
| d="M2.257993 117.980154 415.470783 531.192944 512 627.722161 608.529217 531.192944 1021.742007 117.980154 925.212789 21.450937 512 434.663727 98.787211 21.450937Z"
| fill="#1296db" p-id="5069" />
| </svg>
| </div>
| </el-dialog>
| </div>
| </template>
|
| <script>
| import paint from '@/components/paint/index.vue'
| import graffiti from '@/components/graffiti/index.vue'
| import examinations from '@/components/examinations/index.vue'
| import { getResourcePath } from "@/assets/methods/resources";
| import { getCollectResource, setCollectResource } from "@/assets/methods/resources";
| const handleShow = (num) => {
| const obj = {}
| for (let index = 0; index < num; index++) {
| obj['isShowAnswer' + index] = false
| }
| return obj
| }
| const showObj = handleShow(50)
| export default {
| name: '',
| props: {
| showPageList: {
| type: Array,
| default: [],
| },
| questionData: {
| type: Object,
| },
| },
| components: {examinations,paint,graffiti},
| data() {
| return {
| ...showObj,
| collectImg: require("../../assets/images/icon/heart.png"),
| collectCheck: require("../../assets/images/icon/heart-check.png"),
| isShowExampleOne: false,
| isShowExampleTwo: false,
| isShowExampleThree: false,
| isShowExampleFour: false,
| isShowExampleFive: false,
| dialogVisible: false,
| thinkingDialog: false,
| videoPath: "",
| stepIndex: 1,
| thinkIndex: 1,
| collectResourceList: [],
| chapterData: {
| isCollectImg: false,
| isCollectVideo: false,
| txtOne: "",
| txtTwo: "",
| },
| showIndex:0,
| thinkData:[],
| thinkOne: [
| "1:一个函数是不 是偶函数,可以由 函数的图像是否关 于y 轴 对 称 来 判 断;当函数用解析 法表示时,可以用 偶 函 数 的 定 义 来 判断。 偶函数:一般地，设函数f(x)的定义域为D，如果对于任意xED，都有XED，且f(-x)=f(x)，那么函数f(x)就叫作偶函数",
| "2:计算f(-x)",
| "3:判断f(-x)是否等于f(x)",
| ],
| thinkTwo:[
| '因为<i>AB</i>的长度为<i>x</i>（m），<i>BC</i>的长度为（12-<i>x</i>）（m），所以必须满足<i>x</i>＞0且12-<i>x</i>＞0才有实际意义.'
| ],
| thinkThree:[
| '计算该军舰从出发地驶入海港所需要的时间，就可得到函数<i>s</i>=<i>f</i>（<i>t</i>）的定义域.用解析法表示函数后，再画出函数的图像.'
| ],
| thinkFour:[
| '首先需明确这个函数的定义域.由于居民用电量不同，其收费标准也不同，所以这是分段函数.其次要厘清自变量<i>x</i>在不同的取值范围内与因变量<i>y</i>之间的对应关系，并列出相应的解析式来解决相关问题.'
| ],
| thinkFive:[
| '首先求出小李从A城到B城和从B城返回A城共花费的时间，明确函数的定义域.小李去B城和返回A城的过程中，<i>y</i>与<i>x</i>分别对应的解析式不相同，所以该函数需用分段函数表示.'
| ],
| thinkSix:[
| '首先需要计算备用材料可修建饲养室新墙的总长；因每间饲养室的周长是定值，所以设<i>AB</i>的长为<i>x</i>（m），就可以用含<i>x</i>的代数式表示<i>BC</i>的长；',
| '再用解析法表示总面积<i>y</i>（m<sup>2</sup>）与<i>x</i>（m）的函数关系；然后利用函数的性质来解决问题.'
| ],
| thinkSeven:[
| '先由图像求出一次函数的解析式，',
| '再根据每月所获利润=（销售单价-进价）×每月销售量，列出每月所获利润<i>w</i>与销售单价<i>x</i>的函数关系.'
| ]
| };
| },
| computed: {},
| async mounted() {
| const data = localStorage.getItem("math-chapterData");
| if (data) {
| this.chapterData = JSON.parse(data);
| }
| this.getPath();
| this.collectResourceList = await getCollectResource(this.config.activeBook.bookId)
| },
| methods: {
| async getPath() {
| this.videoPath = await getResourcePath(
| "a28cd862d61b5df2201406b76e9f01b0"
| );
| },
| handleChapterData() {
| localStorage.setItem(
| "math-chapterData",
| JSON.stringify(this.chapterData)
| );
| },
| handleCollect(type) {
| if (type == "img") {
| this.handleCollectResource("722FE833", "", 'images/0101-1.jpg', "图片", "json", '图3-15')
| } else if (type == "video") {
| this.handleCollectResource("a28cd862d61b5df2201406b76e9f01b0", "a28cd862d61b5df2201406b76e9f01b0", '', "视频", "bits", '视频：判数函数奇偶性的方法和步骤')
| }
| this.handleChapterData();
| },
| openMathDiaolog() {
| this.dialogVisible = true;
| },
| openDialog(queryData) {
| this.thinkData = queryData
| this.thinkingDialog = !this.thinkingDialog
| },
| closeDialog() {
| this.showIndex = 0
| },
| changeNext() {
| if (this.showIndex < this.thinkData.length - 1) this.showIndex = this.showIndex + 1
| },
| //资源收藏事件
| handleCollectResource(id, md5, resourcePath, resourceType, source, resourceName) {
| let list = this.collectResourceList
| if (list.findIndex(item => item.id == id) > -1) {
| list = list.filter(item => item.id != id)
| } else {
| list.push({
| id,
| md5,
| resourcePath,
| resourceType,
| source,
| resourceName,
| })
| }
| this.collectResourceList = list
| setCollectResource(this.config.activeBook.bookId, this.collectResourceList)
| }
| },
| }
| </script>
|
| <style lang="less" scoped>
| li {
| list-style: none;
| }
|
| .txt-p {
| margin-top: 0;
| padding: 10px 0;
| }
|
| .bottom-btn {
| display: flex;
| flex-direction: column;
| align-items: center;
| justify-content: center;
| }
|
| .step-num {
| position: relative;
|
| .step-num-box {
| position: absolute;
| top: 16px;
| left: 13px;
| color: #fff;
| }
| }
| </style>
|
|
