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Bei ",[569,1098,1100,1129],{"className":1099},[572],[569,1101,1103],{"className":1102},[576],[578,1104,1105],{"xmlns":580},[582,1106,1107,1126],{},[585,1108,1109,1111,1113,1117,1119,1121,1123],{},[706,1110,708],{},[702,1112,704],{},[588,1114,1116],{"mathvariant":1115},"normal","∣",[588,1118,1048],{},[588,1120,1116],{"mathvariant":1115},[702,1122,704],{},[706,1124,1125],{},"1",[592,1127,1128],{"encoding":594},"0 \u003C |a| \u003C 1",[569,1130,1132,1151,1176],{"className":1131,"ariaHidden":599},[598],[569,1133,1135,1139,1142,1145,1148],{"className":1134},[603],[569,1136],{"className":1137,"style":1138},[607],"height:0.6835em;vertical-align:-0.0391em;",[569,1140,708],{"className":1141},[612],[569,1143],{"className":1144,"style":729},[728],[569,1146,704],{"className":1147},[733],[569,1149],{"className":1150,"style":729},[728],[569,1152,1154,1158,1161,1164,1167,1170,1173],{"className":1153},[603],[569,1155],{"className":1156,"style":1157},[607],"height:1em;vertical-align:-0.25em;",[569,1159,1116],{"className":1160},[612],[569,1162,1048],{"className":1163},[612,613],[569,1165,1116],{"className":1166},[612],[569,1168],{"className":1169,"style":729},[728],[569,1171,704],{"className":1172},[733],[569,1174],{"className":1175,"style":729},[728],[569,1177,1179,1182],{"className":1178},[603],[569,1180],{"className":1181,"style":743},[607],[569,1183,1125],{"className":1184},[612]," wird gestaucht, bei ",[569,1187,1189,1207],{"className":1188},[572],[569,1190,1192],{"className":1191},[576],[578,1193,1194],{"xmlns":580},[582,1195,1196,1204],{},[585,1197,1198,1200,1202],{},[588,1199,1048],{},[702,1201,704],{},[706,1203,708],{},[592,1205,1206],{"encoding":594},"a \u003C 0",[569,1208,1210,1228],{"className":1209,"ariaHidden":599},[598],[569,1211,1213,1216,1219,1222,1225],{"className":1212},[603],[569,1214],{"className":1215,"style":841},[607],[569,1217,1048],{"className":1218},[612,613],[569,1220],{"className":1221,"style":729},[728],[569,1223,704],{"className":1224},[733],[569,1226],{"className":1227,"style":729},[728],[569,1229,1231,1234],{"className":1230},[603],[569,1232],{"className":1233,"style":743},[607],[569,1235,708],{"className":1236},[612]," zusätzlich an der x-Achse gespiegelt.",[620,1239,1240,1269,1270,1273,1274,1396,1397,1449,1450,1501],{},[569,1241,1243,1257],{"className":1242},[572],[569,1244,1246],{"className":1245},[576],[578,1247,1248],{"xmlns":580},[582,1249,1250,1255],{},[585,1251,1252],{},[588,1253,1254],{},"b",[592,1256,1254],{"encoding":594},[569,1258,1260],{"className":1259,"ariaHidden":599},[598],[569,1261,1263,1266],{"className":1262},[603],[569,1264],{"className":1265,"style":648},[607],[569,1267,1254],{"className":1268},[612,613]," wirkt in ",[683,1271,1272],{},"x-Richtung"," umgekehrt: Der Graph wird mit dem Faktor ",[569,1275,1277,1296],{"className":1276},[572],[569,1278,1280],{"className":1279},[576],[578,1281,1282],{"xmlns":580},[582,1283,1284,1293],{},[585,1285,1286],{},[1287,1288,1289,1291],"mfrac",{},[706,1290,1125],{},[588,1292,1254],{},[592,1294,1295],{"encoding":594},"\\frac{1}{b}",[569,1297,1299],{"className":1298,"ariaHidden":599},[598],[569,1300,1302,1306],{"className":1301},[603],[569,1303],{"className":1304,"style":1305},[607],"height:1.1901em;vertical-align:-0.345em;",[569,1307,1309,1314,1392],{"className":1308},[612],[569,1310],{"className":1311},[1312,1313],"mopen","nulldelimiter",[569,1315,1317],{"className":1316},[1287],[569,1318,1322,1383],{"className":1319},[1320,1321],"vlist-t","vlist-t2",[569,1323,1326,1378],{"className":1324},[1325],"vlist-r",[569,1327,1331,1352,1363],{"className":1328,"style":1330},[1329],"vlist","height:0.8451em;",[569,1332,1334,1339],{"style":1333},"top:-2.655em;",[569,1335],{"className":1336,"style":1338},[1337],"pstrut","height:3em;",[569,1340,1346],{"className":1341},[1342,1343,1344,1345],"sizing","reset-size6","size3","mtight",[569,1347,1349],{"className":1348},[612,1345],[569,1350,1254],{"className":1351},[612,613,1345],[569,1353,1355,1358],{"style":1354},"top:-3.23em;",[569,1356],{"className":1357,"style":1338},[1337],[569,1359],{"className":1360,"style":1362},[1361],"frac-line","border-bottom-width:0.04em;",[569,1364,1366,1369],{"style":1365},"top:-3.394em;",[569,1367],{"className":1368,"style":1338},[1337],[569,1370,1372],{"className":1371},[1342,1343,1344,1345],[569,1373,1375],{"className":1374},[612,1345],[569,1376,1125],{"className":1377},[612,1345],[569,1379,1382],{"className":1380},[1381],"vlist-s","​",[569,1384,1386],{"className":1385},[1325],[569,1387,1390],{"className":1388,"style":1389},[1329],"height:0.345em;",[569,1391],{},[569,1393],{"className":1394},[1395,1313],"mclose"," gestreckt. Bei ",[569,1398,1400,1419],{"className":1399},[572],[569,1401,1403],{"className":1402},[576],[578,1404,1405],{"xmlns":580},[582,1406,1407,1416],{},[585,1408,1409,1411,1413],{},[588,1410,1254],{},[702,1412,937],{},[706,1414,1415],{},"2",[592,1417,1418],{"encoding":594},"b = 2",[569,1420,1422,1440],{"className":1421,"ariaHidden":599},[598],[569,1423,1425,1428,1431,1434,1437],{"className":1424},[603],[569,1426],{"className":1427,"style":648},[607],[569,1429,1254],{"className":1430},[612,613],[569,1432],{"className":1433,"style":729},[728],[569,1435,937],{"className":1436},[733],[569,1438],{"className":1439,"style":729},[728],[569,1441,1443,1446],{"className":1442},[603],[569,1444],{"className":1445,"style":743},[607],[569,1447,1415],{"className":1448},[612]," wird er also auf die halbe Breite gestaucht. Bei ",[569,1451,1453,1471],{"className":1452},[572],[569,1454,1456],{"className":1455},[576],[578,1457,1458],{"xmlns":580},[582,1459,1460,1468],{},[585,1461,1462,1464,1466],{},[588,1463,1254],{},[702,1465,704],{},[706,1467,708],{},[592,1469,1470],{"encoding":594},"b \u003C 0",[569,1472,1474,1492],{"className":1473,"ariaHidden":599},[598],[569,1475,1477,1480,1483,1486,1489],{"className":1476},[603],[569,1478],{"className":1479,"style":721},[607],[569,1481,1254],{"className":1482},[612,613],[569,1484],{"className":1485,"style":729},[728],[569,1487,704],{"className":1488},[733],[569,1490],{"className":1491,"style":729},[728],[569,1493,1495,1498],{"className":1494},[603],[569,1496],{"className":1497,"style":743},[607],[569,1499,708],{"className":1500},[612]," wird zusätzlich an der y-Achse gespiegelt.",[565,1503,1504,1505,1572,1573,1601],{},"Ein Punkt ",[569,1506,1508,1535],{"className":1507},[572],[569,1509,1511],{"className":1510},[576],[578,1512,1513],{"xmlns":580},[582,1514,1515,1532],{},[585,1516,1517,1521,1524,1526,1529],{},[702,1518,1520],{"stretchy":1519},"false","(",[588,1522,1523],{},"u",[702,1525,1116],{},[588,1527,1528],{},"v",[702,1530,1531],{"stretchy":1519},")",[592,1533,1534],{"encoding":594},"(u \\mid v)",[569,1536,1538,1559],{"className":1537,"ariaHidden":599},[598],[569,1539,1541,1544,1547,1550,1553,1556],{"className":1540},[603],[569,1542],{"className":1543,"style":1157},[607],[569,1545,1520],{"className":1546},[1312],[569,1548,1523],{"className":1549},[612,613],[569,1551],{"className":1552,"style":729},[728],[569,1554,1116],{"className":1555},[733],[569,1557],{"className":1558,"style":729},[728],[569,1560,1562,1565,1569],{"className":1561},[603],[569,1563],{"className":1564,"style":1157},[607],[569,1566,1528],{"className":1567,"style":1568},[612,613],"margin-right:0.0359em;",[569,1570,1531],{"className":1571},[1395]," auf dem Graphen von ",[569,1574,1576,1589],{"className":1575},[572],[569,1577,1579],{"className":1578},[576],[578,1580,1581],{"xmlns":580},[582,1582,1583,1587],{},[585,1584,1585],{},[588,1586,590],{},[592,1588,590],{"encoding":594},[569,1590,1592],{"className":1591,"ariaHidden":599},[598],[569,1593,1595,1598],{"className":1594},[603],[569,1596],{"className":1597,"style":608},[607],[569,1599,590],{"className":1600,"style":614},[612,613]," wird dabei zum 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3",[569,2495,2497,2524,2542,2587,2605],{"className":2496,"ariaHidden":599},[598],[569,2498,2500,2503,2506,2509,2512,2515,2518,2521],{"className":2499},[603],[569,2501],{"className":2502,"style":1157},[607],[569,2504,1971],{"className":2505,"style":1568},[612,613],[569,2507,1520],{"className":2508},[1312],[569,2510,2404],{"className":2511},[612],[569,2513,1531],{"className":2514},[1395],[569,2516],{"className":2517,"style":729},[728],[569,2519,937],{"className":2520},[733],[569,2522],{"className":2523,"style":729},[728],[569,2525,2527,2530,2533,2536,2539],{"className":2526},[603],[569,2528],{"className":2529,"style":743},[607],[569,2531,1415],{"className":2532},[612],[569,2534],{"className":2535,"style":903},[728],[569,2537,1646],{"className":2538},[907],[569,2540],{"className":2541,"style":903},[728],[569,2543,2545,2549,2578,2581,2584],{"className":2544},[603],[569,2546],{"className":2547,"style":2548},[607],"height:0.8974em;vertical-align:-0.0833em;",[569,2550,2552,2555],{"className":2551},[612],[569,2553,1125],{"className":2554},[612],[569,2556,2558],{"className":2557},[1933],[569,2559,2561],{"className":2560},[1320],[569,2562,2564],{"className":2563},[1325],[569,2565,2567],{"className":2566,"style":1923},[1329],[569,2568,2569,2572],{"style":1945},[569,2570],{"className":2571,"style":1949},[1337],[569,2573,2575],{"className":2574},[1342,1343,1344,1345],[569,2576,1415],{"className":2577},[612,1345],[569,2579],{"className":2580,"style":903},[728],[569,2582,1629],{"className":2583},[907],[569,2585],{"className":2586,"style":903},[728],[569,2588,2590,2593,2596,2599,2602],{"className":2589},[603],[569,2591],{"className":2592,"style":743},[607],[569,2594,1125],{"className":2595},[612],[569,2597],{"className":2598,"style":729},[728],[569,2600,937],{"className":2601},[733],[569,2603],{"className":2604,"style":729},[728],[569,2606,2608,2611],{"className":2607},[603],[569,2609],{"className":2610,"style":743},[607],[569,2612,1990],{"className":2613},[612],[565,2615,2616,2617,1956,2703,2800,2801,2829,2830,2865,2866,2895,2896,3018,3019,1031],{},"Aus ",[569,2618,2620,2654],{"className":2619},[572],[569,2621,2623],{"className":2622},[576],[578,2624,2625],{"xmlns":580},[582,2626,2627,2651],{},[585,2628,2629,2631,2633,2635,2637,2639,2642,2645,2647,2649],{},[588,2630,590],{},[702,2632,1520],{"stretchy":1519},[588,2634,878],{},[702,2636,1531],{"stretchy":1519},[702,2638,937],{},[588,2640,2641],{},"sin",[702,2643,2644],{},"⁡",[702,2646,1520],{"stretchy":1519},[588,2648,878],{},[702,2650,1531],{"stretchy":1519},[592,2652,2653],{"encoding":594},"f(x) = \\sin(x)",[569,2655,2657,2684],{"className":2656,"ariaHidden":599},[598],[569,2658,2660,2663,2666,2669,2672,2675,2678,2681],{"className":2659},[603],[569,2661],{"className":2662,"style":1157},[607],[569,2664,590],{"className":2665,"style":614},[612,613],[569,2667,1520],{"className":2668},[1312],[569,2670,878],{"className":2671},[612,613],[569,2673,1531],{"className":2674},[1395],[569,2676],{"className":2677,"style":729},[728],[569,2679,937],{"className":2680},[733],[569,2682],{"className":2683,"style":729},[728],[569,2685,2687,2690,2694,2697,2700],{"className":2686},[603],[569,2688],{"className":2689,"style":1157},[607],[569,2691,2641],{"className":2692},[2693],"mop",[569,2695,1520],{"className":2696},[1312],[569,2698,878],{"className":2699},[612,613],[569,2701,1531],{"className":2702},[1395],[569,2704,2706,2742],{"className":2705},[572],[569,2707,2709],{"className":2708},[576],[578,2710,2711],{"xmlns":580},[582,2712,2713,2739],{},[585,2714,2715,2717,2719,2721,2723,2725,2727,2729,2731,2733,2735,2737],{},[588,2716,1971],{},[702,2718,1520],{"stretchy":1519},[588,2720,878],{},[702,2722,1531],{"stretchy":1519},[702,2724,937],{},[706,2726,1990],{},[588,2728,2641],{},[702,2730,2644],{},[702,2732,1520],{"stretchy":1519},[706,2734,1415],{},[588,2736,878],{},[702,2738,1531],{"stretchy":1519},[592,2740,2741],{"encoding":594},"g(x) = 3 \\sin(2x)",[569,2743,2745,2772],{"className":2744,"ariaHidden":599},[598],[569,2746,2748,2751,2754,2757,2760,2763,2766,2769],{"className":2747},[603],[569,2749],{"className":2750,"style":1157},[607],[569,2752,1971],{"className":2753,"style":1568},[612,613],[569,2755,1520],{"className":2756},[1312],[569,2758,878],{"className":2759},[612,613],[569,2761,1531],{"className":2762},[1395],[569,2764],{"className":2765,"style":729},[728],[569,2767,937],{"className":2768},[733],[569,2770],{"className":2771,"style":729},[728],[569,2773,2775,2778,2781,2785,2788,2791,2794,2797],{"className":2774},[603],[569,2776],{"className":2777,"style":1157},[607],[569,2779,1990],{"className":2780},[612],[569,2782],{"className":2783,"style":2784},[728],"margin-right:0.1667em;",[569,2786,2641],{"className":2787},[2693],[569,2789,1520],{"className":2790},[1312],[569,2792,1415],{"className":2793},[612],[569,2795,878],{"className":2796},[612,613],[569,2798,1531],{"className":2799},[1395],". Die Amplitude ist ",[569,2802,2804,2817],{"className":2803},[572],[569,2805,2807],{"className":2806},[576],[578,2808,2809],{"xmlns":580},[582,2810,2811,2815],{},[585,2812,2813],{},[706,2814,1990],{},[592,2816,1990],{"encoding":594},[569,2818,2820],{"className":2819,"ariaHidden":599},[598],[569,2821,2823,2826],{"className":2822},[603],[569,2824],{"className":2825,"style":743},[607],[569,2827,1990],{"className":2828},[612],", die Periode halbiert sich von ",[569,2831,2833,2850],{"className":2832},[572],[569,2834,2836],{"className":2835},[576],[578,2837,2838],{"xmlns":580},[582,2839,2840,2847],{},[585,2841,2842,2844],{},[706,2843,1415],{},[588,2845,2846],{},"π",[592,2848,2849],{"encoding":594},"2\\pi",[569,2851,2853],{"className":2852,"ariaHidden":599},[598],[569,2854,2856,2859,2862],{"className":2855},[603],[569,2857],{"className":2858,"style":743},[607],[569,2860,1415],{"className":2861},[612],[569,2863,2846],{"className":2864,"style":1568},[612,613]," auf ",[569,2867,2869,2883],{"className":2868},[572],[569,2870,2872],{"className":2871},[576],[578,2873,2874],{"xmlns":580},[582,2875,2876,2880],{},[585,2877,2878],{},[588,2879,2846],{},[592,2881,2882],{"encoding":594},"\\pi",[569,2884,2886],{"className":2885,"ariaHidden":599},[598],[569,2887,2889,2892],{"className":2888},[603],[569,2890],{"className":2891,"style":776},[607],[569,2893,2846],{"className":2894,"style":1568},[612,613],". Das Maximum liegt bei ",[569,2897,2899,2921],{"className":2898},[572],[569,2900,2902],{"className":2901},[576],[578,2903,2904],{"xmlns":580},[582,2905,2906,2918],{},[585,2907,2908,2910,2912],{},[588,2909,878],{},[702,2911,937],{},[1287,2913,2914,2916],{},[588,2915,2846],{},[706,2917,2404],{},[592,2919,2920],{"encoding":594},"x = \\frac{\\pi}{4}",[569,2922,2924,2942],{"className":2923,"ariaHidden":599},[598],[569,2925,2927,2930,2933,2936,2939],{"className":2926},[603],[569,2928],{"className":2929,"style":776},[607],[569,2931,878],{"className":2932},[612,613],[569,2934],{"className":2935,"style":729},[728],[569,2937,937],{"className":2938},[733],[569,2940],{"className":2941,"style":729},[728],[569,2943,2945,2949],{"className":2944},[603],[569,2946],{"className":2947,"style":2948},[607],"height:1.0404em;vertical-align:-0.345em;",[569,2950,2952,2955,3015],{"className":2951},[612],[569,2953],{"className":2954},[1312,1313],[569,2956,2958],{"className":2957},[1287],[569,2959,2961,3007],{"className":2960},[1320,1321],[569,2962,2964,3004],{"className":2963},[1325],[569,2965,2968,2982,2990],{"className":2966,"style":2967},[1329],"height:0.6954em;",[569,2969,2970,2973],{"style":1333},[569,2971],{"className":2972,"style":1338},[1337],[569,2974,2976],{"className":2975},[1342,1343,1344,1345],[569,2977,2979],{"className":2978},[612,1345],[569,2980,2404],{"className":2981},[612,1345],[569,2983,2984,2987],{"style":1354},[569,2985],{"className":2986,"style":1338},[1337],[569,2988],{"className":2989,"style":1362},[1361],[569,2991,2992,2995],{"style":1365},[569,2993],{"className":2994,"style":1338},[1337],[569,2996,2998],{"className":2997},[1342,1343,1344,1345],[569,2999,3001],{"className":3000},[612,1345],[569,3002,2846],{"className":3003,"style":1568},[612,613,1345],[569,3005,1382],{"className":3006},[1381],[569,3008,3010],{"className":3009},[1325],[569,3011,3013],{"className":3012,"style":1389},[1329],[569,3014],{},[569,3016],{"className":3017},[1395,1313]," mit ",[569,3020,3022,3052],{"className":3021},[572],[569,3023,3025],{"className":3024},[576],[578,3026,3027],{"xmlns":580},[582,3028,3029,3049],{},[585,3030,3031,3033,3045,3047],{},[588,3032,1971],{},[585,3034,3035,3037,3043],{},[702,3036,1520],{"fence":599},[1287,3038,3039,3041],{},[588,3040,2846],{},[706,3042,2404],{},[702,3044,1531],{"fence":599},[702,3046,937],{},[706,3048,1990],{},[592,3050,3051],{"encoding":594},"g\\left(\\frac{\\pi}{4}\\right) = 3",[569,3053,3055,3161],{"className":3054,"ariaHidden":599},[598],[569,3056,3058,3062,3065,3068,3152,3155,3158],{"className":3057},[603],[569,3059],{"className":3060,"style":3061},[607],"height:1.2em;vertical-align:-0.35em;",[569,3063,1971],{"className":3064,"style":1568},[612,613],[569,3066],{"className":3067,"style":2784},[728],[569,3069,3071,3078,3146],{"className":3070},[1671],[569,3072,3074],{"className":3073,"style":1676},[1312,1675],[569,3075,1520],{"className":3076},[1680,3077],"size1",[569,3079,3081,3084,3143],{"className":3080},[612],[569,3082],{"className":3083},[1312,1313],[569,3085,3087],{"className":3086},[1287],[569,3088,3090,3135],{"className":3089},[1320,1321],[569,3091,3093,3132],{"className":3092},[1325],[569,3094,3096,3110,3118],{"className":3095,"style":2967},[1329],[569,3097,3098,3101],{"style":1333},[569,3099],{"className":3100,"style":1338},[1337],[569,3102,3104],{"className":3103},[1342,1343,1344,1345],[569,3105,3107],{"className":3106},[612,1345],[569,3108,2404],{"className":3109},[612,1345],[569,3111,3112,3115],{"style":1354},[569,3113],{"className":3114,"style":1338},[1337],[569,3116],{"className":3117,"style":1362},[1361],[569,3119,3120,3123],{"style":1365},[569,3121],{"className":3122,"style":1338},[1337],[569,3124,3126],{"className":3125},[1342,1343,1344,1345],[569,3127,3129],{"className":3128},[612,1345],[569,3130,2846],{"className":3131,"style":1568},[612,613,1345],[569,3133,1382],{"className":3134},[1381],[569,3136,3138],{"className":3137},[1325],[569,3139,3141],{"className":3140,"style":1389},[1329],[569,3142],{},[569,3144],{"className":3145},[1395,1313],[569,3147,3149],{"className":3148,"style":1676},[1395,1675],[569,3150,1531],{"className":3151},[1680,3077],[569,3153],{"className":3154,"style":729},[728],[569,3156,937],{"className":3157},[733],[569,3159],{"className":3160,"style":729},[728],[569,3162,3164,3167],{"className":3163},[603],[569,3165],{"className":3166,"style":743},[607],[569,3168,1990],{"className":3169},[612],[565,3171,3172,3173,3282,3283,3311,3312,3464,3465,3493],{},"Bei ",[569,3174,3176,3213],{"className":3175},[572],[569,3177,3179],{"className":3178},[576],[578,3180,3181],{"xmlns":580},[582,3182,3183,3210],{},[585,3184,3185,3187,3189,3191,3193,3195,3197,3199,3201,3203,3205,3208],{},[588,3186,1971],{},[702,3188,1520],{"stretchy":1519},[588,3190,878],{},[702,3192,1531],{"stretchy":1519},[702,3194,937],{},[588,3196,590],{},[702,3198,1520],{"stretchy":1519},[706,3200,1415],{},[588,3202,878],{},[702,3204,881],{},[706,3206,3207],{},"6",[702,3209,1531],{"stretchy":1519},[592,3211,3212],{"encoding":594},"g(x) = f(2x - 6)",[569,3214,3216,3243,3270],{"className":3215,"ariaHidden":599},[598],[569,3217,3219,3222,3225,3228,3231,3234,3237,3240],{"className":3218},[603],[569,3220],{"className":3221,"style":1157},[607],[569,3223,1971],{"className":3224,"style":1568},[612,613],[569,3226,1520],{"className":3227},[1312],[569,3229,878],{"className":3230},[612,613],[569,3232,1531],{"className":3233},[1395],[569,3235],{"className":3236,"style":729},[728],[569,3238,937],{"className":3239},[733],[569,3241],{"className":3242,"style":729},[728],[569,3244,3246,3249,3252,3255,3258,3261,3264,3267],{"className":3245},[603],[569,3247],{"className":3248,"style":1157},[607],[569,3250,590],{"className":3251,"style":614},[612,613],[569,3253,1520],{"className":3254},[1312],[569,3256,1415],{"className":3257},[612],[569,3259,878],{"className":3260},[612,613],[569,3262],{"className":3263,"style":903},[728],[569,3265,881],{"className":3266},[907],[569,3268],{"className":3269,"style":903},[728],[569,3271,3273,3276,3279],{"className":3272},[603],[569,3274],{"className":3275,"style":1157},[607],[569,3277,3207],{"className":3278},[612],[569,3280,1531],{"className":3281},[1395]," klammert man zuerst den Faktor vor ",[569,3284,3286,3299],{"className":3285},[572],[569,3287,3289],{"className":3288},[576],[578,3290,3291],{"xmlns":580},[582,3292,3293,3297],{},[585,3294,3295],{},[588,3296,878],{},[592,3298,878],{"encoding":594},[569,3300,3302],{"className":3301,"ariaHidden":599},[598],[569,3303,3305,3308],{"className":3304},[603],[569,3306],{"className":3307,"style":776},[607],[569,3309,878],{"className":3310},[612,613]," aus: ",[569,3313,3315,3362],{"className":3314},[572],[569,3316,3318],{"className":3317},[576],[578,3319,3320],{"xmlns":580},[582,3321,3322,3359],{},[585,3323,3324,3326,3328,3330,3332,3334,3336,3338,3340,3342,3345,3347,3349,3351,3353,3355,3357],{},[588,3325,590],{},[702,3327,1520],{"stretchy":1519},[706,3329,1415],{},[588,3331,878],{},[702,3333,881],{},[706,3335,3207],{},[702,3337,1531],{"stretchy":1519},[702,3339,937],{},[588,3341,590],{},[702,3343,1520],{"fence":599,"stretchy":599,"minsize":3344,"maxsize":3344},"1.2em",[706,3346,1415],{},[702,3348,1520],{"stretchy":1519},[588,3350,878],{},[702,3352,881],{},[706,3354,1990],{},[702,3356,1531],{"stretchy":1519},[702,3358,1531],{"fence":599,"stretchy":599,"minsize":3344,"maxsize":3344},[592,3360,3361],{"encoding":594},"f(2x - 6) = f\\bigl(2(x - 3)\\bigr)",[569,3363,3365,3392,3413,3446],{"className":3364,"ariaHidden":599},[598],[569,3366,3368,3371,3374,3377,3380,3383,3386,3389],{"className":3367},[603],[569,3369],{"className":3370,"style":1157},[607],[569,3372,590],{"className":3373,"style":614},[612,613],[569,3375,1520],{"className":3376},[1312],[569,3378,1415],{"className":3379},[612],[569,3381,878],{"className":3382},[612,613],[569,3384],{"className":3385,"style":903},[728],[569,3387,881],{"className":3388},[907],[569,3390],{"className":3391,"style":903},[728],[569,3393,3395,3398,3401,3404,3407,3410],{"className":3394},[603],[569,3396],{"className":3397,"style":1157},[607],[569,3399,3207],{"className":3400},[612],[569,3402,1531],{"className":3403},[1395],[569,3405],{"className":3406,"style":729},[728],[569,3408,937],{"className":3409},[733],[569,3411],{"className":3412,"style":729},[728],[569,3414,3416,3419,3422,3428,3431,3434,3437,3440,3443],{"className":3415},[603],[569,3417],{"className":3418,"style":3061},[607],[569,3420,590],{"className":3421,"style":614},[612,613],[569,3423,3425],{"className":3424},[1312],[569,3426,1520],{"className":3427},[1680,3077],[569,3429,1415],{"className":3430},[612],[569,3432,1520],{"className":3433},[1312],[569,3435,878],{"className":3436},[612,613],[569,3438],{"className":3439,"style":903},[728],[569,3441,881],{"className":3442},[907],[569,3444],{"className":3445,"style":903},[728],[569,3447,3449,3452,3455,3458],{"className":3448},[603],[569,3450],{"className":3451,"style":3061},[607],[569,3453,1990],{"className":3454},[612],[569,3456,1531],{"className":3457},[1395],[569,3459,3461],{"className":3460},[1395],[569,3462,1531],{"className":3463},[1680,3077],". Der Graph wird also auf die halbe Breite gestaucht und um ",[569,3466,3468,3481],{"className":3467},[572],[569,3469,3471],{"className":3470},[576],[578,3472,3473],{"xmlns":580},[582,3474,3475,3479],{},[585,3476,3477],{},[706,3478,1990],{},[592,3480,1990],{"encoding":594},[569,3482,3484],{"className":3483,"ariaHidden":599},[598],[569,3485,3487,3490],{"className":3486},[603],[569,3488],{"className":3489,"style":743},[607],[569,3491,1990],{"className":3492},[612]," nach rechts verschoben.",[560,3495,3497],{"id":3496},"typische-fehler","Typische Fehler",[617,3499,3500,3602,3821,3931],{},[620,3501,3502,3503,3569,3570,2264,3598,3601],{},"Die Richtung der x-Verschiebung verwechseln: ",[569,3504,3506,3530],{"className":3505},[572],[569,3507,3509],{"className":3508},[576],[578,3510,3511],{"xmlns":580},[582,3512,3513,3527],{},[585,3514,3515,3517,3519,3521,3523,3525],{},[588,3516,590],{},[702,3518,1520],{"stretchy":1519},[588,3520,878],{},[702,3522,881],{},[706,3524,1990],{},[702,3526,1531],{"stretchy":1519},[592,3528,3529],{"encoding":594},"f(x - 3)",[569,3531,3533,3557],{"className":3532,"ariaHidden":599},[598],[569,3534,3536,3539,3542,3545,3548,3551,3554],{"className":3535},[603],[569,3537],{"className":3538,"style":1157},[607],[569,3540,590],{"className":3541,"style":614},[612,613],[569,3543,1520],{"className":3544},[1312],[569,3546,878],{"className":3547},[612,613],[569,3549],{"className":3550,"style":903},[728],[569,3552,881],{"className":3553},[907],[569,3555],{"className":3556,"style":903},[728],[569,3558,3560,3563,3566],{"className":3559},[603],[569,3561],{"className":3562,"style":1157},[607],[569,3564,1990],{"className":3565},[612],[569,3567,1531],{"className":3568},[1395]," ist um ",[569,3571,3573,3586],{"className":3572},[572],[569,3574,3576],{"className":3575},[576],[578,3577,3578],{"xmlns":580},[582,3579,3580,3584],{},[585,3581,3582],{},[706,3583,1990],{},[592,3585,1990],{"encoding":594},[569,3587,3589],{"className":3588,"ariaHidden":599},[598],[569,3590,3592,3595],{"className":3591},[603],[569,3593],{"className":3594,"style":743},[607],[569,3596,1990],{"className":3597},[612],[683,3599,3600],{},"rechts"," verschoben, nicht nach links.",[620,3603,3172,3604,3675,3676,3704,3705,3792,3793,1031],{},[569,3605,3607,3633],{"className":3606},[572],[569,3608,3610],{"className":3609},[576],[578,3611,3612],{"xmlns":580},[582,3613,3614,3630],{},[585,3615,3616,3618,3620,3622,3624,3626,3628],{},[588,3617,590],{},[702,3619,1520],{"stretchy":1519},[706,3621,1415],{},[588,3623,878],{},[702,3625,881],{},[706,3627,3207],{},[702,3629,1531],{"stretchy":1519},[592,3631,3632],{"encoding":594},"f(2x - 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",[569,3677,3679,3692],{"className":3678},[572],[569,3680,3682],{"className":3681},[576],[578,3683,3684],{"xmlns":580},[582,3685,3686,3690],{},[585,3687,3688],{},[706,3689,3207],{},[592,3691,3207],{"encoding":594},[569,3693,3695],{"className":3694,"ariaHidden":599},[598],[569,3696,3698,3701],{"className":3697},[603],[569,3699],{"className":3700,"style":743},[607],[569,3702,3207],{"className":3703},[612]," ablesen: Erst nach dem Ausklammern zu ",[569,3706,3708,3738],{"className":3707},[572],[569,3709,3711],{"className":3710},[576],[578,3712,3713],{"xmlns":580},[582,3714,3715,3735],{},[585,3716,3717,3719,3721,3723,3725,3727,3729,3731,3733],{},[588,3718,590],{},[702,3720,1520],{"fence":599,"stretchy":599,"minsize":3344,"maxsize":3344},[706,3722,1415],{},[702,3724,1520],{"stretchy":1519},[588,3726,878],{},[702,3728,881],{},[706,3730,1990],{},[702,3732,1531],{"stretchy":1519},[702,3734,1531],{"fence":599,"stretchy":599,"minsize":3344,"maxsize":3344},[592,3736,3737],{"encoding":594},"f\\bigl(2(x - 3)\\bigr)",[569,3739,3741,3774],{"className":3740,"ariaHidden":599},[598],[569,3742,3744,3747,3750,3756,3759,3762,3765,3768,3771],{"className":3743},[603],[569,3745],{"className":3746,"style":3061},[607],[569,3748,590],{"className":3749,"style":614},[612,613],[569,3751,3753],{"className":3752},[1312],[569,3754,1520],{"className":3755},[1680,3077],[569,3757,1415],{"className":3758},[612],[569,3760,1520],{"className":3761},[1312],[569,3763,878],{"className":3764},[612,613],[569,3766],{"className":3767,"style":903},[728],[569,3769,881],{"className":3770},[907],[569,3772],{"className":3773,"style":903},[728],[569,3775,3777,3780,3783,3786],{"className":3776},[603],[569,3778],{"className":3779,"style":3061},[607],[569,3781,1990],{"className":3782},[612],[569,3784,1531],{"className":3785},[1395],[569,3787,3789],{"className":3788},[1395],[569,3790,1531],{"className":3791},[1680,3077]," sieht man die Verschiebung um ",[569,3794,3796,3809],{"className":3795},[572],[569,3797,3799],{"className":3798},[576],[578,3800,3801],{"xmlns":580},[582,3802,3803,3807],{},[585,3804,3805],{},[706,3806,1990],{},[592,3808,1990],{"encoding":594},[569,3810,3812],{"className":3811,"ariaHidden":599},[598],[569,3813,3815,3818],{"className":3814},[603],[569,3816],{"className":3817,"style":743},[607],[569,3819,1990],{"className":3820},[612],[620,3822,3823,3851,3852,3880,3881,3930],{},[569,3824,3826,3839],{"className":3825},[572],[569,3827,3829],{"className":3828},[576],[578,3830,3831],{"xmlns":580},[582,3832,3833,3837],{},[585,3834,3835],{},[588,3836,1254],{},[592,3838,1254],{"encoding":594},[569,3840,3842],{"className":3841,"ariaHidden":599},[598],[569,3843,3845,3848],{"className":3844},[603],[569,3846],{"className":3847,"style":648},[607],[569,3849,1254],{"className":3850},[612,613]," wie ",[569,3853,3855,3868],{"className":3854},[572],[569,3856,3858],{"className":3857},[576],[578,3859,3860],{"xmlns":580},[582,3861,3862,3866],{},[585,3863,3864],{},[588,3865,1048],{},[592,3867,1048],{"encoding":594},[569,3869,3871],{"className":3870,"ariaHidden":599},[598],[569,3872,3874,3877],{"className":3873},[603],[569,3875],{"className":3876,"style":776},[607],[569,3878,1048],{"className":3879},[612,613]," behandeln: ",[569,3882,3884,3906],{"className":3883},[572],[569,3885,3887],{"className":3886},[576],[578,3888,3889],{"xmlns":580},[582,3890,3891,3903],{},[585,3892,3893,3895,3897,3899,3901],{},[588,3894,590],{},[702,3896,1520],{"stretchy":1519},[706,3898,1415],{},[588,3900,878],{},[702,3902,1531],{"stretchy":1519},[592,3904,3905],{"encoding":594},"f(2x)",[569,3907,3909],{"className":3908,"ariaHidden":599},[598],[569,3910,3912,3915,3918,3921,3924,3927],{"className":3911},[603],[569,3913],{"className":3914,"style":1157},[607],[569,3916,590],{"className":3917,"style":614},[612,613],[569,3919,1520],{"className":3920},[1312],[569,3922,1415],{"className":3923},[612],[569,3925,878],{"className":3926},[612,613],[569,3928,1531],{"className":3929},[1395]," ist in x-Richtung gestaucht, nicht gestreckt.",[620,3932,3933,3934,4126,4127,4213],{},"Die Reihenfolge in y-Richtung vertauschen: ",[569,3935,3937,3981],{"className":3936},[572],[569,3938,3940],{"className":3939},[576],[578,3941,3942],{"xmlns":580},[582,3943,3944,3978],{},[585,3945,3946,3948,3950,3952,3958,3960,3962,3964,3966,3968,3974,3976],{},[706,3947,1415],{},[702,3949,1646],{},[702,3951,1520],{"stretchy":1519},[1878,3953,3954,3956],{},[588,3955,878],{},[706,3957,1415],{},[702,3959,1629],{},[706,3961,1125],{},[702,3963,1531],{"stretchy":1519},[702,3965,937],{},[706,3967,1415],{},[1878,3969,3970,3972],{},[588,3971,878],{},[706,3973,1415],{},[702,3975,1629],{},[706,3977,1415],{},[592,3979,3980],{"encoding":594},"2 \\cdot (x^2 + 1) = 2x^2 + 2",[569,3982,3984,4002,4049,4070,4117],{"className":3983,"ariaHidden":599},[598],[569,3985,3987,3990,3993,3996,3999],{"className":3986},[603],[569,3988],{"className":3989,"style":743},[607],[569,3991,1415],{"className":3992},[612],[569,3994],{"className":3995,"style":903},[728],[569,3997,1646],{"className":3998},[907],[569,4000],{"className":4001,"style":903},[728],[569,4003,4005,4008,4011,4040,4043,4046],{"className":4004},[603],[569,4006],{"className":4007,"style":2064},[607],[569,4009,1520],{"className":4010},[1312],[569,4012,4014,4017],{"className":4013},[612],[569,4015,878],{"className":4016},[612,613],[569,4018,4020],{"className":4019},[1933],[569,4021,4023],{"className":4022},[1320],[569,4024,4026],{"className":4025},[1325],[569,4027,4029],{"className":4028,"style":1923},[1329],[569,4030,4031,4034],{"style":1945},[569,4032],{"className":4033,"style":1949},[1337],[569,4035,4037],{"className":4036},[1342,1343,1344,1345],[569,4038,1415],{"className":4039},[612,1345],[569,4041],{"className":4042,"style":903},[728],[569,4044,1629],{"className":4045},[907],[569,4047],{"className":4048,"style":903},[728],[569,4050,4052,4055,4058,4061,4064,4067],{"className":4051},[603],[569,4053],{"className":4054,"style":1157},[607],[569,4056,1125],{"className":4057},[612],[569,4059,1531],{"className":4060},[1395],[569,4062],{"className":4063,"style":729},[728],[569,4065,937],{"className":4066},[733],[569,4068],{"className":4069,"style":729},[728],[569,4071,4073,4076,4079,4108,4111,4114],{"className":4072},[603],[569,4074],{"className":4075,"style":2548},[607],[569,4077,1415],{"className":4078},[612],[569,4080,4082,4085],{"className":4081},[612],[569,4083,878],{"className":4084},[612,613],[569,4086,4088],{"className":4087},[1933],[569,4089,4091],{"className":4090},[1320],[569,4092,4094],{"className":4093},[1325],[569,4095,4097],{"className":4096,"style":1923},[1329],[569,4098,4099,4102],{"style":1945},[569,4100],{"className":4101,"style":1949},[1337],[569,4103,4105],{"className":4104},[1342,1343,1344,1345],[569,4106,1415],{"className":4107},[612,1345],[569,4109],{"className":4110,"style":903},[728],[569,4112,1629],{"className":4113},[907],[569,4115],{"className":4116,"style":903},[728],[569,4118,4120,4123],{"className":4119},[603],[569,4121],{"className":4122,"style":743},[607],[569,4124,1415],{"className":4125},[612]," ist etwas anderes als ",[569,4128,4130,4154],{"className":4129},[572],[569,4131,4133],{"className":4132},[576],[578,4134,4135],{"xmlns":580},[582,4136,4137,4151],{},[585,4138,4139,4141,4147,4149],{},[706,4140,1415],{},[1878,4142,4143,4145],{},[588,4144,878],{},[706,4146,1415],{},[702,4148,1629],{},[706,4150,1125],{},[592,4152,4153],{"encoding":594},"2x^2 + 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In der Formel wird erst gestreckt, dann verschoben.",{"title":4215,"searchDepth":4216,"depth":4216,"links":4217},"",2,[4218,4219,4220],{"id":562,"depth":4216,"text":563},{"id":1850,"depth":4216,"text":1851},{"id":3496,"depth":4216,"text":3497},[4222,4225,4229,4232,4235,4237,4240],{"lhs":4223,"rhs":4224},"a*(b*((u\u002Fb + c) - c))^3 + d","a*u^3 + d",{"lhs":4226,"rhs":1125,"where":4227},"2*(x - 3)^2 + 1",{"x":4228},3,{"lhs":4226,"rhs":1990,"where":4230},{"x":4231},4,{"lhs":4233,"rhs":4234},"3*sin(2*(x + pi))","3*sin(2*x)",{"lhs":4236,"rhs":1990},"3*sin(2*(pi\u002F4))",{"lhs":4238,"rhs":4239},"2*x - 6","2*(x - 3)",{"lhs":4241,"rhs":4242},"2*(x^2 + 1)","2*x^2 + 2","a \\neq 0,\\ b \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a \\neq 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b \\neq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan 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