/R7 6.48 Tf f 1598 4563.67 6 225 re (2 )Tj 3.72 0 Td /R15 9.96 Tf (2)Tj /R7 9.98676 Tf 7.92 0 Td Q ()Tj 1 0 0 1 128.64 502.16 Tm Q 2933 2280.67 l ET [( )-2.63158(3)-5.26316(\))333]TJ 3931 1178.67 m ( )Tj ET 27 0 R [(\()-3.44695(x)7.3486(\))-3.44695( )-2.33512(=)-0.748061( )-2.33512(x)500]TJ (x)Tj /R7 9.975 Tf q h [(9)-5.26316(\))-3.84164(,)-2.63158( )-2.63158(S)556]TJ /R7 9.975 Tf 2.52 0 Td (t)Tj /R7 9.99984 Tf 4531 465.668 l 10.92 4.56 Td (1)Tj 900 920.668 l 130.44 4.56 Td [(d)-4.00824(\))-3.00539( )-326.009(\()]TJ 4658.33 -3024.66 l 2898 3569.67 6 6 re /R15 9.96 Tf S Q /R7 9.98676 Tf 8.33333 0 0 8.33333 0 0 cm BT 3822 4651.67 m Q 2979 4948.67 m /R7 9.975 Tf 1707 5868.67 l /R7 6.48 Tf /R7 6.48 Tf q /R7 9.98676 Tf 8.28 -7.32 Td 1 0 0 1 98.4 468.32 Tm /R7 9.99984 Tf f 821 2651.67 l 841 4562.67 m [( )-2.33439(x)500]TJ 18.48 4.56 Td 1 0 0 1 331.56 372.92 Tm f (3)Tj (3)Tj ()Tj f (2)Tj 3.72 0 Td 3.24 -4.56 Td Q 3.24 -4.56 Td [( )-2.37067(2)-4.74134(x)500]TJ ()Tj 3.24 -4.56 Td 2189 3463.67 6 6 re (,)Tj 1682 5939.67 m 8.33333 0 0 8.33333 0 0 cm BT 2.52 0 Td /R7 9.975 Tf (x)Tj /R15 9.96 Tf [( )-2.33512(2)-4.66731(t)1.634(x)7.3486( )-2.33512(+)-0.748061( )-2.33512(t)278]TJ /R22 9.98676 Tf 7.44 0 Td 3.24 -4.56 Td ET /R7 9.975 Tf /R7 9.98676 Tf ( )Tj [(\()-4.35041(x)6.0241(\))-4.35041( )-3.01205(=)-2.26492( )-3.01205(x)500]TJ >> 0.12 0 0 -0.12 324.24 565.08 Tm [( )-1169.55( )]TJ /R7 10.0134 Tf S (2)Tj ()Tj f S 821 1259.67 l ()Tj S (3)Tj 2764 1069.67 l ( )Tj 384 2538.67 6 94 re [(2 )250]TJ /R7 9.98532 Tf /R7 6.48 Tf ( )Tj W n 7.92 0 Td 1 j 3427 1094.67 l 2997 4045.67 l 1 J 1014 4257.67 584 6 re q 0.12 0 0 -0.12 243.12 760.44 Tm 7.92 0 Td 3.24 -4.56 Td 26 0 obj 3323 3326.67 l 1 0 0 1 394.68 256.64 Tm 2672 1808.67 m q 9.36 -7.32 Td /R7 9.975 Tf /R7 9.98532 Tf 8.33333 0 0 8.33333 0 0 cm BT 7.92 0 Td 7.44 0 Td S ( )Tj /R15 9.96 Tf 1014 3032.67 584 6 re 817 2547.67 l /R7 6.48 Tf /R15 9.96 Tf 2665 3083.67 m /R7 9.99984 Tf 2195 2632.67 348 6 re [(\()-3.44695(0)500]TJ 1 0 0 1 141.84 495.8 Tm (3)Tj 4390 4560.67 l 2.52 0 Td [( )-2.33512(2)-4.66731(t)1.634(\))-3.44695(x)7.3486( )-2.33512(+)-0.748061( )-2.33512(t)278]TJ f S q /R7 9.99984 Tf -289.92 -19.44 Td 229.32 0 Td 49.68 4.56 Td 59.16 4.56 Td 10.92 0 Td 2.52 0 Td [( )-2.00394(= )250]TJ 19.08 -1.56 Td /R7 9.975 Tf [(3 )250]TJ (1)Tj ET 8.33333 0 0 8.33333 0 0 cm BT 37.68 -1.2 Td 1 0 0 1 340.56 545.6 Tm Q 2543 2838.67 6 94 re 10.2 -1.56 Td 2048 5721.67 l ET ET 23.16 4.56 Td 384 3475.67 6 94 re 7.92 0 Td 1999 1455.67 l /R7 6.48 Tf 1604 2732.67 585 6 re f [( )-2.33512(t)1.634(\))-3.44695(x)500]TJ ()Tj (3)Tj /R7 6.48 Tf f 30 4.56 Td (1)Tj 3785 3235.67 l Q h 2.52 0 Td 3.24 -4.56 Td 838 1958.67 m ET 4.92 -4.56 Td f 3.24 1.56 Td 1604 4457.67 585 6 re 4.92 4.56 Td /R7 9.98676 Tf 2898 3857.67 6 6 re /R7 9.975 Tf 2705 2870.67 l 1289 3410.67 m 2.52 0 Td 1242 4684.67 l ( )Tj S (t)Tj [( )-3.01205(k)6.0241(o)-6.0241(m)18.9636(m)18.9636(t)0.89126( )-3.01205(v)6.0241(o)-6.0241(n)6.0241( )-3.01205(u)6.0241(n)6.0241(t)0.89126(e)-1.78252(n)6.0241( )-3.01205(u)6.0241(n)6.0241(d)-6.0241( )-3.01205(g)6.0241(e)-1.78252(h)6.0241(t)0.89126( )-3.01205(n)6.0241(a)-1.78252(c)-1.78105(h)6.0241( )-3.01205(o)-6.0241(b)-6.0241(e)-1.78252(n)6.0241(\))-4.35091( )]TJ /R15 9.96 Tf 3.24 1.56 Td 8.256 w Q /R7 9.99984 Tf 4.92 -4.56 Td 2713 5168.67 l f Hier eine Übersicht über weitere ganzrationale Funktionen, darin Links zu weiteren Aufgaben. /R7 9.98676 Tf 1008 2738.67 6 94 re (2)Tj [(4 )250]TJ /R7 9.98676 Tf 3825 1098.67 m /R7 9.99984 Tf 48.72 -1.56 Td (4)Tj 3.24 -4.56 Td /R7 9.98676 Tf 3.24 -4.56 Td (3)Tj q ET Q 4.92 -4.56 Td q /R15 9.96 Tf 1 0 0 1 401.76 502.16 Tm 1 0 0 1 129.24 133.28 Tm 12.48 4.56 Td 2672 4258.67 m [( )-2.00394(6)-4.00788(\))-3.00591( )-2.00394(:)1.99515( )-2.00394(\()-3.00591(x)7.99232( )-2.00394(+ )-2.00394(2)-4.00788(\))-3.00539( )]TJ /R7 9.98676 Tf 4.92 -4.56 Td 2543 2532.67 6 6 re ()Tj 8.04 -1.56 Td (x)Tj Q [(a)-0.651347(u)7.27631(b)-4.74134(i)1.59609(l)1.59609(d)-4.74134(e)-0.651347(r)-3.48559( )250]TJ [( )-2.37067(3)-4.74134(x)500]TJ Kurvendiskussion einer ganzrationalen Funktion einfach erklärt Aufgaben mit Lösungen Zusammenfassung als PDF Jetzt kostenlos dieses Thema lernen! [( )-2.00394(1)-4.00788(1)-4.00788(x)7.99232( )-2.00394(+ )-2.00394(6)-4.00788(\))-3.00591( )-2.00394(:)1.99515( )-2.00394(\()-3.00591(x)7.99232( )250]TJ f /R7 9.98676 Tf 3.24 -4.56 Td 1 0 0 1 360.12 360.56 Tm /R7 9.98676 Tf 1 0 0 1 393.72 480.68 Tm /R15 9.96 Tf (2)Tj 7.92 0 Td 10.8 0 Td /R15 9.96 Tf 110.16 4.56 Td 7.92 0 Td /R7 9.975 Tf /R36 9.99516 Tf f (1)Tj T*[(B)-5.98792(e)-0.652814(s)4.43547(t)1.59389(i)1.59389(m)20.8886(m)20.8886(e)-0.652814( )-146.582(a)-0.652814(l)1.59389(l)1.59389(e)-0.652814( )-146.582(A)12.9587(c)-0.652814(h)7.27631(s)4.43473(e)-0.652814(n)7.27631(s)4.43473(c)-0.652814(h)7.27631(n)7.27631(i)1.59463(t)1.59463(t)1.59463(p)-4.74134(u)7.27631(n)7.27631(k)7.27631(t)1.59463(e)-0.652814( )-146.582(u)7.27631(n)7.27631(d)-4.74134( )-146.581(d)-4.74134(i)1.59463(e)-0.652814( )-146.582(g)7.27631(e)-0.652814(m)20.8871(e)-0.651347(i)1.59316(n)7.27631(s)4.4362(a)-0.651347(m)]TJ 2731 4258.67 l 2921 1922.67 m [( )-2.37067(t)1.59316(\))-3.49439( )-2.37067(+)-0.830321( )-2.37067(2)-4.74102( )]TJ q 12.48 4.56 Td /R7 9.98676 Tf W n f 2.52 0 Td (2)Tj 2543 3132.67 6 6 re ( )Tj /R7 10.0134 Tf 44.64 4.56 Td /R7 9.98676 Tf [( )-2.33512(2)-4.66731(t)1.634(\))-3.44695(x)7.3486( )250]TJ -311.16 -18.96 Td (x)Tj 81.6 4.56 Td f 1 0 0 1 141.48 545.6 Tm /R7 9.98676 Tf ()Tj 16.92 4.56 Td (1)Tj /R11 1 Tf /R15 9.96 Tf endobj BI q /R7 9.98676 Tf 10.92 0 Td 3.24 -4.56 Td 8.33333 0 0 8.33333 0 0 cm BT [(\()-3.49365(x)7.27631(\))-3.49365( )-2.37067(=)-0.829587( )-2.37067(4)-4.74134(t)1.59389(x)500]TJ (2)Tj 3.24 1.56 Td /R15 9.96 Tf 1 0 0 1 448.68 549.32 Tm Substitution (nur bei biquadratischen Funktionen f(x) = a x 4 + b x² + c) IV. 384 2638.67 6 94 re 37.2 0 Td [( )-2.37067(2)-4.74134(x)7.27662( )-13486.2(h)7.27631(\))-3.49401( )-338.865(f)8.52326(\()-3.49439(x)7.27631(\))-3.49439( )-2.37067(=)-0.830321( )-2.37067(\()-3.49439(x)500]TJ 8.33333 0 0 8.33333 0 0 cm BT 7.92 0 Td ET 49.08 4.56 Td [(x)7.34787( )-2.33439(+)-0.748061( )-2.33439(1)-4.66829( )-15623(e)-0.589648(\))-3.44696( )-386.844(f)8.56896(\()-3.44695(x)7.3486(\))-3.44695( )-2.33512(=)-0.748061( )250]TJ ET 84.6 0 Td ()Tj /R7 9.99984 Tf 7.92 0 Td (2)Tj Q /R7 6.48 Tf [(5)-5.26316(\))-3.84164( )-2.63158(u)6.76692(n)6.76692(d)-5.26316( )-2.63158(S)556]TJ Q f 25.68 4.56 Td 1516 4655.67 l (t)Tj 3.24 1.56 Td /R7 9.99984 Tf 2664 3426.67 m /R7 6.48 Tf (3)Tj 77.76 4.56 Td /R7 9.98676 Tf S [( )-2.00394(3)-4.00788(x)7.99232( )250]TJ (3)Tj 1 0 0 1 369.6 314.36 Tm 768 1476.67 m 1 0 0 1 212.52 495.8 Tm 1329 1263.67 l (3)Tj [( )-2.33439(6)-4.66805(x)500]TJ h /R7 6.48 Tf 176.4 0 Td h ()Tj 100.44 -1.56 Td /R7 6.48 Tf 3.24 -4.56 Td W n ()Tj ET (3)Tj [( )-230.008(v)7.99232(o)-4.00788(n)7.99232( )-230.008(t)1.99515( )-230.008(au)7.99232(f)8.99428( )-230.008(d)-4.00788(i)1.99808(e )-230.008(F)3.9903(o)-4.00788(r)-3.00591(m)21.9906( )-230.008(d)-4.00788(es)4.99227( )250]TJ 1 0 0 1 317.4 523.76 Tm /R7 9.99984 Tf f (6)Tj 3.36 0 Td h ()Tj 2.52 0 Td (3)Tj 1348 5946.67 l 21 0 Td (2)Tj 145.08 -1.56 Td [( )-2.63158(+)-1.41345( )-2.63158(4)-5.26316(x)500]TJ 1.8 1.56 Td /R7 9.99984 Tf W n Q /R7 9.96 Tf q /R7 10.0134 Tf f 1 0 0 1 398.16 640.16 Tm ()Tj (2)Tj /R36 9.99516 Tf 8.33333 0 0 8.33333 0 0 cm BT /R15 9.96 Tf 8.28 -7.32 Td f 10.92 0 Td 44.64 4.56 Td 8.28 -1.56 Td /R7 9.98676 Tf (3)Tj W n 23.16 0 Td 1083 1542.67 l 8.28 -6.36 Td Q /R7 9.96 Tf /R7 9.975 Tf 1 0 0 1 240.72 677.72 Tm f 34.32 0 Td 2779 5855.67 l /R7 6.48 Tf 12.48 4.56 Td (x)Tj /R7 9.98532 Tf 1 0 0 1 454.56 325.76 Tm 2.52 0 Td @�p3�KEPN6M��sa�� �@)h�e0��҂.hDFƊ9�����C�DHh6� � 8 �3 ����'��=� yV��A��m2�L���o9�(�D@p9N�QuI[� H 0� � ]�> ��ޭϫm����Fv�lA i���l �+K��z �\0%8Jrg�%�� o @�8 4496 3944.67 l /R7 6.48 Tf /R7 6.48 Tf q 1008 2532.67 6 6 re /R15 9.96 Tf /R7 6.48 Tf 7.92 0 Td /R7 9.99984 Tf /R7 9.98532 Tf (4)Tj q (5)Tj /R7 9.98676 Tf [(2)-3.32587(x)500]TJ q 2855 4555.67 l /R7 9.975 Tf 1695 5630.67 l /R15 9.96 Tf ( )Tj ()Tj 35 0 obj ()Tj /R7 9.98676 Tf (3)Tj [(4)-1074.08(t)278]TJ /R7 6.48 Tf (4)Tj (t)Tj 77.64 -1.56 Td q (3)Tj /R7 6.48 Tf [()-0.105892()]TJ /R7 6.48 Tf 2.28 -3 Td (2)Tj /R7 6.48 Tf 2.52 0 Td [( )-2.33439(+)-0.748061( )-2.33439(5)-4.66805(x)500]TJ /R7 9.96 Tf /W 83 [(c)-1.11277(\))-3.84214( )-387.594(f)8.18771(\()-3.84237(x)6.76692(\))-3.84237( )-2.63158(=)-1.41345( )-2.63158(2)-5.26316(x)500]TJ ET h [(3 )250]TJ /R7 9.98676 Tf 1 0 0 1 321.48 373.88 Tm 3815 4560.67 l Q q 0] Q /R7 9.98532 Tf [(+)-0.748061( )-2.33366(0)-4.66878(,)-2.33366(5)-4.66878(x)500]TJ ( )Tj 4.92 -4.56 Td /R7 9.96 Tf [(1)-6.0241(,)-3.01205(8)-6.0241(5)-6.0241(9)-6.0241(3)-6.0241(7)-6.0241(5)-6.02416( )]TJ /R8 9.96 Tf 167.88 4.56 Td 2898 4794.67 6 6 re [( )-2.33366(6)-4.66878( )-2.33366(z)-0.588181(u)7.34713( )-2.33366(P)-8.74791(\()-3.44548(2)500]TJ /R7 6.48 Tf 1356 1542.67 m [( )-3.01205(t)0.89126(x)500]TJ (4)Tj 3403.16 -2968.36 l /R7 9.975 Tf h (4)Tj /R7 6.48 Tf 7.92 0 Td y = mx P 2 | 1 Bestimme den Funktionsterm f(x). 1 0 0 1 50.4 342.92 Tm 7.92 0 Td 1 0 0 1 123.24 314.12 Tm 7.92 0 Td 7.92 0 Td [( )-2.33366(8)-4.66829( )-3931.54(h)7.3486(\))-3.44696( )-338.781(f)]TJ 1598 4800.67 6 94 re 1 0 0 1 50.4 366.92 Tm 3.24 -4.56 Td /R7 6.48 Tf ET Q /R7 6.48 Tf (Definition pdf) Nullstellenbestimmung durch Ausklammern Polynomdivision , Spezialfall: ax^n+e , Substitution Übungsaufgaben -1- , Lösung Übungsaufgaben -2- , Lösung Übungsaufgaben -3- , Lösung Übungsaufgaben -4- , Lösung S 4390 4651.67 m 19.08 4.56 Td (3)Tj /R8 9.96 Tf 4.92 -4.56 Td q ET [(3 )250]TJ 2.52 0 Td 1.8 1.56 Td ()Tj /R7 6.48 Tf [(1)-5.26316(,)-2.63158(8)-5.26316(6)-5.26316(0)-5.26316(9)-5.26316(3)-5.26316(7)-5.26316(5)-5.26321( )-2565.04(1)-5.26316(,)-2.63158(8)-5.26316(6)-5.26316(2)-5.26316(5)-5.26321( )-5548.5(x)6.76692( )-3780.08( )]TJ q 23.16 4.56 Td 1 0 0 1 336.12 556.16 Tm 8.04 -1.56 Td 8.33333 0 0 8.33333 0 0 cm BT (x)Tj /R7 6.48 Tf /R7 6.48 Tf q q ()Tj (4)Tj 8.33333 0 0 8.33333 0 0 cm BT q 0.952057 0 0 -1.04794 0 0 cm 8.33333 0 0 8.33333 0 0 cm BT [( )-2.00394(= )-2.00394(2)-4.00788( )-2.00394(u)7.99232(n)7.99232(d)-4.00788( )-2.00404(P)-8.00843(\()-3.00591(0)-4.00788(|)19.9969(4)-4(\))-3.00591( )-8750.14(f)8.99428(\))-3.00539( )-506.012(n)7.99232( )-2.00394(= )-2.00394(4)-4.00788(,)-2.00394( )-2.00394(x)500.008]TJ 3.24 1.56 Td 8.33333 0 0 8.33333 0 0 cm BT /R7 9.98676 Tf q q /R7 6.48 Tf 3784 3082.67 l 33.96 -1.56 Td 3.24 -4.56 Td Q 15.84 4.56 Td q 8.33333 0 0 8.33333 0 0 cm BT /R15 9.96 Tf 1.8 1.56 Td /R7 9.98676 Tf (1)Tj [(,)-3.01205( )-231.928(w)23.2051(i)0.89126(e)-1.78252( )-231.928(s)3.45915(i)0.89126(c)-1.78252(h)6.0241( )250]TJ 7.92 0 Td 1598 4788.67 6 6 re q 837 1133.67 m /R7 9.98532 Tf f ( )Tj ()Tj 2189 4257.67 6 6 re /R7 9.96 Tf f (2)Tj Q ()Tj 8.33333 0 0 8.33333 0 0 cm BT 1 0 0 1 170.76 421.04 Tm 2189 3032.67 6 6 re 1008 3038.67 6 94 re /R7 6.48 Tf /R7 9.98676 Tf (2)Tj S 4.92 -4.56 Td q 8.33333 0 0 8.33333 0 0 cm BT /R7 6.48 Tf Q 3739 4651.67 m Q (t)Tj /R7 9.98532 Tf ( )Tj 1.8 1.56 Td 2.52 0 Td /R7 10.0134 Tf 1 0 0 1 492 129.44 Tm [(\()-3.44695(1)500]TJ ET 1604 4557.67 585 6 re 4.92 4.56 Td 1 0 0 1 105 372.92 Tm 4530 559.668 m S /R7 9.99984 Tf -390.48 -12.36 Td f /R7 10.0134 Tf /R7 9.96 Tf 7.92 0 Td ( )Tj [( )-2.33439(2)-4.66878(\))333]TJ /R7 6.48 Tf /R7 9.975 Tf (3)Tj 2733 2372.67 l /R7 9.98676 Tf 8.33333 0 0 8.33333 0 0 cm BT endstream 162 -1.56 Td 2189 2638.67 6 94 re ()Tj 3240 3326.67 l 7.92 0 Td 1 0 0 1 321.72 193.88 Tm /R7 6.48 Tf (3)Tj 10.92 4.56 Td 8.33333 0 0 8.33333 0 0 cm BT (1)Tj W n /R7 9.98676 Tf ( )Tj 4.92 -4.56 Td /R7 9.975 Tf 1 0 0 1 161.4 133.28 Tm ET ()Tj /R7 9.975 Tf ET f 234.96 0 Td ( )Tj 3.24 -4.56 Td f Q 2733 2171.67 l /R15 9.96 Tf 883 1026.67 l -87.48 -11.52 Td 3852 1069.67 l [(4 )250]TJ 2543 3857.67 6 6 re [(x)6.0241( )]TJ ()Tj [( )-3.01205(x)6.0241(\))-4.35041( )-3.01205(f)7.69778(�)6.0241(r)-4.35041( )-3.01205(a)-1.78252( )250]TJ endobj 1.8 1.56 Td ( )Tj endobj f [(:)1.30845( )-2.63158(x)500]TJ 2�LuH�^�[����q��Z�W���`�V{ ����R[=��v�\q�)�*�4�R8�\�t�J�Ys�:&n2��1���o���T Q (2)Tj /R7 6.48 Tf q 3.24 1.56 Td /R7 9.98676 Tf f -135.12 -12.36 Td ( )Tj (2)Tj 1 0 0 1 110.04 294.92 Tm /R7 9.96 Tf 4.92 4.56 Td ()Tj 1 0 0 1 325.8 377.48 Tm /R7 9.99984 Tf (3)Tj ()Tj f Q /R15 9.96 Tf h ()Tj <> (2)Tj 81.96 4.56 Td 2662 1828.67 l 1.68 -4.56 Td /Subtype/Type3>> 0 G f [(1)-4.66878(\))-3.44548( )-6611.08(i)1.634(\))-3.44696( )-555.067(f)]TJ [( )-3.01205(1)-6.0241(\))-4.34944( )-12231.9(k)6.0241(\))-4.34944( )-340.361(f)]TJ Q q ()Tj 38.16 0 Td q [(\()-3.44548(0)500]TJ Q 2543 3138.67 6 94 re ��d�!$�i:����S2�LƓq��e9�Χ#�@b2�‡��@d4��2 �,�ͦ�*M�'���e3M�s��8�m2��CA���$��f&����a���&�9���1�| 27.24 4.56 Td ET W n -419.76 -26.04 Td /R15 9.96 Tf q 1 0 0 1 383.28 390.32 Tm 4531 465.668 l /R7 9.98676 Tf 1694 1541.67 l /R7 6.48 Tf ()Tj 11.4 TL S [(\()-4.35041(x)500]TJ -411.6 -11.4 Td 1 0 0 1 458.64 390.32 Tm ( )Tj (x)Tj 2681 2625.67 m h 0.12 0 0 -0.12 174.96 545.64 Tm 2557 5946.67 l ( )Tj 3.24 -4.56 Td 12 0 Td /R7 9.98532 Tf [( )-2.33366(5)-4.66878(\))-3.44553( )-6839.39(j)-10.3819(\))-3.44696( )-543.051(f)8.56896(\()-3.44695(x)7.3486(\))-3.44695( )-2.33512(=)-0.748061( )250]TJ /R7 9.99984 Tf /R7 6.48 Tf 11.64 0 Td -354.48 -12.36 Td 1 0 0 1 543.6 58.2802 Tm /R7 6.48 Tf ET [( )-2.63158(1)-5.26316(\))333]TJ 1730 6074.67 m [(4)-4.00788(\))-3.00591( )-2.00394(f)8.99428(�)7.99232(r)-3.00591( )-2.00394(t)1.99515( )250]TJ Q 1008 4357.67 6 6 re q ()Tj 3 2.04 Td /R7 6.48 Tf 28 0 obj (2)Tj [(g)7.27631(\))-3.49401( )-338.865(f)8.52326(\()-3.49439(x)7.27631(\))-3.49439( )-2.37067(=)-0.830321( )-2.37067(\()-3.49439(x)7.27631( )250]TJ /R7 9.98676 Tf h 1014 3132.67 584 6 re 1 0 0 1 359.64 487.88 Tm ()Tj ()Tj 1 0 0 1 98.4 455.96 Tm (1)Tj [(A)-0.891628(u)1.78326(f)-4.34967(g)-6.0241(a)-6.0241(b)1.78326(e)-1.78326( )-3.01205(4)-6.02416(:)-4.34967( )-3.01205(P)-3.45768(o)-6.0241(l)0.89126(y)-6.0241(n)1.78252(o)-6.0241(m)25.7715(d)1.78252(i)0.89126(v)-6.0241(i)0.89126(s)3.45768(i)0.89126(o)-6.0241(n)1.78306( )]TJ /R7 10.0134 Tf /R7 9.98676 Tf Q 2195 2532.67 348 6 re /R15 9.96 Tf 1 0 0 1 271.2 758.36 Tm 1289 4668.67 l h /R15 9.96 Tf 8.33333 0 0 8.33333 0 0 cm BT ( )Tj 2673 3083.67 m (1)Tj [(3)-4.66878(\))-3.44548( )-7812.68(j)-10.3819(\))-3.44696( )-543.051(f)]TJ ET S 0.12 0 0 -0.12 95.76 145.68 Tm 31.68 4.56 Td ()Tj Q [(x)6.76692(\()-3.84164(x)500]TJ [(n)7.3486(e)-0.589648(h)7.3486(m)20.9985(e)-0.589648(n)7.3486(,)-2.33512( )-2.33512(d)-4.66731(a)-0.589648(m)21.0014(i)1.634(t)1.634( )-2.33512(f)8.56896(\()-3.44695(x)7.3486(\))-3.44695( )-2.33512(=)-0.748061( )-2.33512(a)-0.589648(x)500]TJ 1 0 0 1 327.72 314.12 Tm f [(a)-0.652814(\))-3.49401( )-386.935(f)8.52399(\()-3.49365(x)7.27631(\))-3.49365( )-2.37067(=)-0.829587( )-2.37067(x)500]TJ [(e)-0.586714(n)7.34566(d)-4.67025(e)-0.586714(r)-3.44401(m)20.9985(a)-0.586714(�)-4.67025(e)-0.586714(n)7.34566( )250]TJ 1 0 0 1 475.2 468.32 Tm /R7 9.975 Tf /R7 6.48 Tf (t)Tj 7.92 4.56 Td Bestimme die ganzrationale Funktion kleinsten Grades, deren Graph punktsymmetrisch zum Koordinatenursprung verläuft und den Terrassenpunkt besitzt. /R15 9.96 Tf ()Tj ()Tj /R15 9.96 Tf 2.52 0 Td /R7 6.48 Tf /R7 9.98532 Tf ()Tj /R7 9.98676 Tf 2189 2632.67 6 6 re ()Tj /R7 6.48 Tf 3.24 -4.56 Td 190.32 0 Td [( )-2.00394(= )-2.00394(2)-4.00788(,)-2.00394( )-2.00404(x)]TJ q [( )-2.00394(3)-4.00788(x)500.008]TJ (2)Tj [( )-2.37067(+)-0.829587( )-2.37067(x)500]TJ 1 0 0 1 92.88 155 Tm (r)Tj /R7 10.0134 Tf ( )Tj [()-1.39425()316.406]TJ /R7 9.98532 Tf (3)Tj 1 0 0 1 378.36 545.6 Tm /R7 9.99984 Tf 2673 5168.67 m q 1481 4164.67 l h [( )-2.63158(5)-5.26316(x)500]TJ Q [(,)-2.00394( )-230.008(w)25.9897(i)1.99515(e )-230.008(s)4.9952(i)1.99515(ch)7.99232( )250]TJ /R7 6.48 Tf f [( )-2.63158(+)-1.41418( )-2.63158(2)-5.26316(x)6.76692( )250]TJ [(+)-0.748061( )-2.33439(6)-4.66805(x)500]TJ 1692 5944.67 m W n 8.33333 0 0 8.33333 0 0 cm BT [(2 )250]TJ (1)Tj 100.68 0 Td Q 3517 4066.67 l f 1 0 0 1 338.64 129.44 Tm 1.8 1.56 Td Q [(2 )250]TJ 2762 1069.67 l 4.92 4.56 Td (4)Tj 4.92 -4.56 Td -4.2 -4.56 Td 83 0 0 -36 83 -6 d1 3.72 0 Td /R15 9.96 Tf 4.92 -4.56 Td 19.08 -1.56 Td ()Tj [( )-2.00394(= )-2.00394(2)-4.00788(,)-2.00394( )-2.00394(x)500.008]TJ <>stream 7.92 0 Td (2)Tj /R7 9.96 Tf q /R7 6.48 Tf (3)Tj /R7 6.48 Tf /BPC 1 q 12.48 4.56 Td [( )-2.33366(+)-0.748061( )-2.33366(6)-4.66878(x)500]TJ (t)Tj /R15 9.96 Tf f /R7 9.98532 Tf /R7 6.48 Tf 1 0 0 1 184.44 229.76 Tm /R7 6.48 Tf 2.52 0 Td 0 G f Q 7.92 0 Td f 3883 4199.67 l h [( )-2.37067(+)-0.828854( )-2.37067(4)-4.74134(x)7.27631( )-2.37067(+)-0.828854( )-2.37067(1)-4.74134(6)-4.74102( )-2225.63(d)-4.74134(\))-3.49401( )-326.847(f)8.52326(\()-3.49439(x)7.27631(\))-3.49439( )-2.37067(=)-0.830321( )250]TJ [( )-2.00394(+ )-2.00394(1)-4.00788(2)-4.00788(x)7.99232( )-2.00394(+ )-2.00394(1)-4.00788(4)-4.00788(\))-3.00591( )-2.00394(:)1.99515( )-2.00394(\()-3.00591(x)8( )]TJ 220.8 0 Td ()Tj [(2)-5.26316(x)500]TJ /R7 9.98676 Tf ()Tj ()Tj 1 0 0 1 138.36 372.92 Tm /R7 9.98676 Tf /R7 9.975 Tf [( )-2.33366(2)-4.66829( )-7308.01(f)8.56896(\))-3.44696( )-507.003(f)8.56896(\()-3.44695(x)7.3486(\))-3.44695( )-2.33512(=)-0.748061( )-2.33512(t)1.634(x)500]TJ (1)Tj /R7 9.98532 Tf 1 J /R7 6.48 Tf 8.33333 0 0 8.33333 0 0 cm BT 3082 4617.67 l W n /R7 9.975 Tf )-2.00394( )-230.008(B)-5.01131(es)4.99373(ch)7.99232(r)-3.00591(ei)1.99515(b)-4.00788(e )250]TJ 60 0 0 34 0 0 cm 8.33333 0 0 8.33333 0 0 cm BT (3)Tj q 1 0 0 1 149.04 405.56 Tm /R15 9.96 Tf /R7 10.0134 Tf Berechnen Sie die Nullstellen folgender Funktionen. q (2)Tj 5.04 0 Td 2941 3082.67 m f f 2724 2883.67 l /R15 9.96 Tf ()Tj Q /R7 9.99984 Tf [(4)-4.2735(.)2.13675(5)-4.27356(. ()Tj /R7 9.975 Tf W n endobj Q 1 0 0 1 153 112.88 Tm ET 33.12 0 Td S Q /R7 9.975 Tf 1 0 0 1 359.16 443.6 Tm h 43 0 obj /R15 9.96 Tf h /R7 9.98676 Tf (3)Tj [( )-2.33512(3)-4.66731(a)-0.589648(x)7.3486( )-2.33512(+)-0.748061( )-2.33512(1)-4.66731(8)-4.66731(a)-0.589648( )-2.33414( )]TJ 16 0 obj 7.92 0 Td h 7.92 0 Td 4100 1152.67 l /R7 9.975 Tf 1 0 0 1 422.64 495.8 Tm /R15 9.96 Tf 8.33333 0 0 8.33333 0 0 cm BT 2006 5721.67 m 0] /R7 9.98676 Tf ( )Tj 1014 4557.67 584 6 re ET 1 0 0 1 365.04 261.2 Tm (4)Tj 123.96 -1.56 Td 1 0 0 1 72.84 402.2 Tm 8.33333 0 0 8.33333 0 0 cm BT ET 1 0 0 1 141.96 624.68 Tm 1 0 0 1 437.04 545.6 Tm q 17.52 4.56 Td 4141.56 -2683.04 l Q 7.08 -6.36 Td [(1)7.34713(0)500]TJ (r)Tj [(b)-4.66841(\))-3.44553( )-326.764(f)8.57043(\()-3.44548(x)7.34787(\))-3.44548( )-2.33439(=)-0.748061( )-2.33414(x)]TJ ( )Tj T*[(a)-0.588548(\))-3.44553( )-386.843(f)8.57043(\()-3.44548(x)7.34787(\))-3.44548( )-2.33439(=)-0.748061( )-2.33439(x)500]TJ /R7 9.99984 Tf Q [(0)-6.0241(,)-3.01205(2)-6.0241(5)-6.02416( )]TJ ET 67.08 4.56 Td 4.92 4.56 Td ET f [(1/)0.221535(2)500]TJ /R7 9.98676 Tf (3)Tj T*[(a)-1.78326(\))-4.34944( )-388.554(f)7.69852(\()-4.34967(x)6.0241(\))-4.34967( )-3.01205(=)-2.26492( )-3.01205(\()-4.34967(x)6.0241( )-3.01205(+)-2.26492( )-3.01205(2)-6.0241(\))333]TJ Gebrochen Rationale Funktionen W. Kippels 26. 2722 2979.67 l /R7 6.48 Tf /R7 6.48 Tf f [( )-2.37067(4)-4.74102( )-10073.2(l)1.59316(\))-3.49439( )-555.182(f)]TJ [( )-2.33439(x)500]TJ [()-1.39425()316.406]TJ [( )-2.33512(t)278]TJ ()Tj S /R15 9.96 Tf 74.88 0.12 Td /R7 9.975 Tf 2898 3963.67 6 94 re [( )-2.33512(+)-0.748061( )-2.33512(b)-4.66731(x)7.3486( )-2.33512(+)-0.748061( )-2.33512(c)-0.588731( )]TJ W n 1 0 0 1 462.36 325.76 Tm ET ()Tj 8.33333 0 0 8.33333 0 0 cm BT 3.24 -4.56 Td ( )Tj ()Tj ET 1 0 0 1 326.88 229.76 Tm 8.33333 0 0 8.33333 0 0 cm BT [( )-1.61471(\()-2.48643(x)8.75222( )-1.61471(+)0.862936( )-1.61471(2)-3.22943(\))333]TJ /R8 9.96 Tf Q /R7 6.48 Tf 8.33333 0 0 8.33333 0 0 cm BT 3.24 -4.56 Td 25.44 -1.56 Td /R15 9.96 Tf 1481 4139.67 l /R7 9.975 Tf q /F/CCF 57.72 0 Td [( )-2.33512(1)-4.66829( )-2.33512(f)8.56896(�)7.3486(r)-3.44695( )-2.33512(t)1.634( )250]TJ /R7 9.975 Tf T*[(A)-0.891628(u)1.78326(f)-4.34967(g)-6.0241(a)-6.0241(b)1.78326(e)-1.78326( )-3.01205(7)-6.02416(:)-4.34967( )-3.01205(g)-6.0241(e)-1.78326(m)25.7708(e)-1.78326(i)0.89126(n)1.78252(s)3.45768(a)-6.0241(m)25.7715(e)-1.78252( )-3.01205(P)-3.45768(u)1.78252(n)1.78252(k)13.8307(t)-4.34894(e)-1.78319( )]TJ <> 3.24 -4.56 Td

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