()Tj 0.12 0 0 -0.12 346.68 602.16 Tm Diese und weitere Unterrichtsmaterialien können Sie in unserem Shop kaufen. -33.72 -12.36 Td 1 0 0 1 159.6 148.88 Tm 2898 4463.67 6 94 re /R7 6.48 Tf S Q 3785 4560.67 l 3.24 -4.56 Td /R7 9.98676 Tf 3.24 -4.56 Td ()Tj q 2890 2026.67 l /R15 9.96 Tf [( )-2.33439(5)-4.66805(x)500]TJ /R7 10.0134 Tf [(+)0.754848( )-1.6633(1)-3.32513(2)-3.32513(x)500]TJ -411.96 -11.4 Td [( )-2.37067(2)-4.74134(t)1.59316(\))-3.49439(x)500]TJ q 1 0 0 1 76.08 385.28 Tm 1 0 0 1 213.84 133.28 Tm 8.4 0 Td 4466 3235.67 l (3)Tj /R15 9.96 Tf /R7 9.98676 Tf [( )-2.63158(2)-5.26316(x)500]TJ f /R15 9.96 Tf q [(3 )250]TJ 1 0 0 1 199.08 502.16 Tm ()Tj 3.24 -4.56 Td f 1 0 0 1 357.96 229.76 Tm [( )-266.008(u)7.99232(n)7.99232(d)-4.00788( )-266.008(s)4.9952(k)7.99232(i)1.99808(zzi)1.99808(er)-3.00591(e )-266.008(i)1.99808(h)7.99232(r)-3.00591(e )250]TJ 3247 4560.67 l Q /R7 9.98676 Tf f /R7 9 Tf [( )-2.63158(8)-5.26316(\))-3.84164( )-2.63158(=)-1.41271( )-2.63158(\()-3.84164(x)6.76692( )250]TJ /R7 6.48 Tf T*[(a\))-3.00539( )-386.01(n)7.99232( )-2.00394(= )-2.00394(1)-4(,)-2.00394( )-2.00394(x)]TJ /R7 9.98676 Tf 2711 3095.67 l ( )Tj /R7 9.98676 Tf 28 0 obj 145.8 0.12 Td ( )Tj 8.33333 0 0 8.33333 0 0 cm BT f ET q 1 0 0 1 348.6 466.76 Tm endobj (3)Tj ( )Tj 3403.16 -2968.36 l 24.36 0 Td /R7 6.48 Tf 821 2195.67 l 1604 3569.67 585 6 re -336.36 -12.36 Td [()-1.39425()316.406]TJ 36 0 obj /R7 6.48 Tf W n /R7 10.0134 Tf 3.24 -4.56 Td 2.52 0 Td 1615 5168.67 m (3)Tj 3.24 -4.56 Td /R7 9.99984 Tf 1 0 0 1 327.6 584.96 Tm 2006 5292.67 l /R7 9.99984 Tf f /R7 9.975 Tf f 3001 2171.67 l 1 0 0 1 327.96 368.96 Tm -322.92 -27.96 Td f 2658 3320.67 m 2.16 1.56 Td 817 1246.67 l /R15 9.96 Tf f /R7 6.48 Tf /R7 6.48 Tf /R7 9.975 Tf /R7 6.48 Tf 2195 4794.67 703 6 re /R7 9.98676 Tf 10.92 4.56 Td [(\()-4.34967(x)6.0241( )-3.01205(+)-2.26492( )-3.01205(2)-6.0241(\))333]TJ ()Tj f 2543 3957.67 6 6 re [( )-2.33512(2)-4.66731(t)1.634(x)7.3486( )-2.33512(+)-0.748061( )-2.33512(t)278]TJ /R7 6.48 Tf 4.92 4.56 Td [(,)-2.00394( )-230.008(w)25.9897(i)1.99515(e )-230.008(s)4.9952(i)1.99515(ch)7.99232( )250]TJ 3.72 0 Td 1598 2638.67 6 94 re /R7 6.48 Tf [( )-2.00394(= )-2.00394(2)-4.00788(,)-2.00394( )-2.00404(x)]TJ ()Tj [(0)-5.26316(,)-2.63158(2)-5.26316(5)-5.26316(6)-5.26316(2)-5.26316(5)-5.26321( )-5295.87( )]TJ (\()Tj 8.33333 0 0 8.33333 0 0 cm BT 7.92 4.56 Td ()Tj (1)Tj /R7 6.48 Tf 1598 4063.67 6 94 re 0 g [( )-2.33512(t)1.634(\))332.999]TJ 8.04 -1.56 Td 1072 4258.67 m 3.24 -4.56 Td endobj Q ()Tj /R7 9.98676 Tf Q [(2 )250]TJ /R7 6.48 Tf f f endobj /R7 9.98676 Tf 2195 4457.67 348 6 re 8.33333 0 0 8.33333 0 0 cm BT /R15 9.96 Tf [()-1.39425()316.406]TJ 488.16 0 Td [(7)-4.66878(x)7.34713( )-2.33366(+)-0.748061( )-2.33366(1)-4.66878(2)-4.66829( )-10360(e)-0.589648(\))-3.44696( )-386.844(f)8.56896(\()-3.44695(x)7.3486(\))-3.44695( )-2.33512(=)-0.748061( )250]TJ 1.8 1.56 Td 3.24 -4.56 Td ET 117.72 -1.56 Td [(0)-4.66878(\))-3.44548(,)-2.33366( )-2.33366(P)556]TJ 8.33333 0 0 8.33333 0 0 cm BT 1 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)-3.01205(+)-2.26492( )-3.01205(2)-6.0241(\))333]TJ 4496 4018.67 m 4.92 4.56 Td 1 0 0 1 415.68 510.8 Tm W n Um das Verhalten im Unendlichen einer ganzrationalen Funktion zu untersuchen, muss lediglich der Term mit der höchsten Potenz herangezogen werden (Vorzeichen beachten). ()Tj 4.92 4.56 Td /R7 6.48 Tf 7.92 0 Td 1695 5630.67 l [(a)-0.588548(\))-3.44553( )-386.843(f)8.57043(\()-3.44548(x)7.34787(\))-3.44548( )-2.33439(=)-0.748061( )250]TJ (t)Tj 1008 3957.67 6 6 re 18.96 -1.56 Td 12.36 TL [( )-2.63158(1)-5.26316(\))-3.84164( )-2.63158(\()-3.84164(x)500]TJ -387.12 -11.28 Td 384 3569.67 6 6 re /R7 9.96 Tf ET /R7 9.99984 Tf Q 19.08 -1.56 Td ()Tj f ()Tj 3427 1003.67 l ()Tj [(3 )250]TJ 7.92 0 Td 1 0 0 1 395.52 502.16 Tm 1 0 0 1 377.52 466.76 Tm q 0.952057 0 0 -1.04794 0 0 cm /R7 9.98676 Tf 12.48 4.56 Td [(+)-0.748061( )-2.33512(\()-3.44695(2)-4.66731( )250]TJ q 4.92 -4.56 Td /R7 9.98676 Tf 24 0 obj ( )Tj 2.52 0 Td [(a)-1.11277(\))-3.84214( )-387.594(f)8.18771(\()-3.84237(x)6.76692( )-2.63158(+)-1.41345( )-2.63158(1)-5.26316(\))-3.84237( )-2.63158(=)-1.41345( )-2.63158(x)500]TJ /R8 9.96 Tf /R7 9.99984 Tf q /R8 9.96 Tf Q 3115 4272.67 l 1.8 1.56 Td q Q 2898 2732.67 6 6 re (3)Tj (3)Tj 1014 3957.67 584 6 re [( )-2.33512(+)-0.748061( )-2.33512(\()-3.44695(t)278]TJ T*[(A)-0.891628(u)1.78326(f)-4.34967(g)-6.0241(a)-6.0241(b)1.78326(e)-1.78326( )-3.01205(8)-6.02416(:)-4.34967( )-3.01205(N)-0.891996(u)1.78326(l)0.89126(l)0.89126(s)3.45768(t)-4.34894(e)-1.78252(l)0.89126(l)0.89126(e)-1.78252(n)1.78252(b)1.78252(e)-1.78252(s)3.45768(t)-4.34894(i)0.89126(m)25.7715(m)25.7715(u)1.78252(n)1.78252(g)-6.0241( )-3.01205(m)25.7715(i)0.89126(t)-4.34894( )-3.01205(d)1.78399(e)-1.78252(m)25.7715( )-3.01205(I)3.45768(n)1.78252(t)-4.35041(e)-1.78252(r)-1.78252(v)-6.0241(a)-6.0241(l)0.89126(l)0.89126(h)]TJ /R7 9.98676 Tf 1 0 0 1 161.28 120.8 Tm 1 0 0 1 383.28 390.32 Tm [(d)-4.00824(\))-3.00539( )-326.009(\()]TJ ( )Tj 1.8 1.56 Td S [(\()-4.34894(x)6.0241( )250]TJ Q /R15 9.96 Tf (3)Tj endobj 21.12 0 Td 2195 2732.67 348 6 re /R15 9.96 Tf 3.24 -4.56 Td 74.88 0.12 Td q (x)Tj /R15 9.96 Tf /R15 9.96 Tf 3.24 -4.56 Td 7.92 0 Td 1 0 0 1 95.04 234.32 Tm 1.8 1.56 Td Q /R7 6.48 Tf 1 0 0 1 369.6 314.36 Tm ()Tj [()-2106.24()-2526.85()-1685.62()777.999]TJ 7.92 0 Td 8.33333 0 0 8.33333 0 0 cm BT f 2543 2938.67 6 94 re f /R7 6.48 Tf /R15 9.96 Tf q h 1329 1239.67 l 7.92 0 Td q f ET /R15 9.96 Tf (x)Tj 4658.33 -3024.66 l /R7 9.975 Tf Lösungen zu den Aufgaben zu ganzrationalen Funktionen Aufgabe 1: Normalform und Verhalten für x ± a) f(x) = −x5 + 6x 2 − 7x + 12 e) f(x) = − 4x 2 + tx + 12 für t ∈ ℝ b) f(x) = 8x 6 − 12x 5 + 0,5x 4 − x 3 − 2 f) f(x) = tx 3 − 2x 2 + 5x − 1 für t ∈ ℝ c) f(x) = x … (2)Tj 2189 3238.67 6 225 re [( )-2.33366(4)-4.66878(x)7.34713( )-2.33366(+)-0.748061( )-2.33366(1)-4.66878(2)-4.66829( )-10672.5(g)7.3486(\))-3.44696( )-338.781(f)]TJ 2733 1098.67 m