/R7 9.98676 Tf /R7 9.975 Tf [(\()-3.44695(x)7.3486(\))-3.44695( )-2.33512(=)-0.748061( )-2.33512(x)500]TJ /R7 6.48 Tf q ( )Tj /R7 9.98676 Tf 1 0 0 1 370.8 283.64 Tm ET 2195 4457.67 348 6 re f 4.92 4.56 Td endobj 3875 1160.67 l Q /R7 6.48 Tf 74.88 0.12 Td S T*[(A)-0.891628(u)1.78326(f)-4.34967(g)-6.0241(a)-6.0241(b)1.78326(e)-1.78326( )-3.01205(1)-6.0241(0)-6.02416(:)-4.34967( )-3.01205(S)1.78326(y)-6.0241(m)25.7715(m)25.7715(e)-1.78252(t)-4.34894(r)-1.78252(i)0.89126(e)444]TJ /R7 6.48 Tf 775 1155.67 l (x)Tj 7.92 0 Td [(3 )250]TJ Q ( )Tj [( )-2.00394(= )-2.00394(1)-4.00788(,)-2.00394( )-2.00404(x)]TJ /R7 6.48 Tf Q (2)Tj [(a)-0.588548(\))-3.44553( )-386.843(f)8.57043(\()-3.44548(x)7.34787(\))-3.44548( )-2.33439(=)-0.748061( )250]TJ Ggf. 8.33333 0 0 8.33333 0 0 cm BT ( )Tj (3)Tj [( )-2.33512(2)-4.66731(x)500]TJ (3)Tj /R7 9.975 Tf 1008 3232.67 6 6 re ET 7.92 0 Td 3.24 -4.56 Td /R11 1 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 -358.32 -19.44 Td /R7 10.0134 Tf 30.48 4.56 Td /R7 6.48 Tf /R11 1 Tf 3485 4322.67 l /R7 9.975 Tf Q -261.36 -12.36 Td 1 0 0 1 246.48 443.6 Tm 2724 2977.67 l [( )-2.37067(2)-4.74102( )-2.37067( )]TJ W n 133.92 0 Td ( )Tj [( )-2.63158(4)-5.26316(\))-3.84164(\()-3.84164(x)6.76692( )-2.63158(+)-1.41359( )-2.63158(2)-5.26316(\))-3.84214( )]TJ 4.92 4.56 Td h (x)Tj 8.33333 0 0 8.33333 0 0 cm BT 1014 4257.67 584 6 re /R7 9.98676 Tf -291.48 -11.28 Td (x)Tj 7.08 -6.36 Td 1 0 0 1 351.72 502.16 Tm ET /R7 9.98676 Tf q 3.24 -4.56 Td /R7 6.48 Tf 3825 1098.67 m 7.92 0 Td (1)Tj W n 3.24 -4.56 Td 1 0 0 1 50.4 306.92 Tm 18.12 4.56 Td 43 0 obj 1 0 0 1 138.36 372.92 Tm [( )-2.33512(0)-4.67024( )]TJ 2.52 0 Td 2672 2744.67 m ()Tj 1615 5168.67 m [(9)-5.26316(\))-3.84164(,)-2.63158( )-2.63158(S)556]TJ ()Tj [(1)-6.0241(;)0.89126( )-3.01205(0)-6.0241(})-1.92664( )]TJ /R7 6.48 Tf 10.92 4.56 Td 2898 4794.67 6 6 re S Q 384 4157.67 6 6 re (4)Tj Q 1098 1566.67 l (1)Tj 11.64 0 Td 1 0 0 1 50.4 504.32 Tm 1 0 0 1 173.52 360.56 Tm [(x)-1689.47(x)500]TJ h ( )Tj 8.4 0 Td S S Q 7.92 0 Td 1598 3032.67 6 6 re 2195 2532.67 348 6 re /R7 9.975 Tf 1604 2532.67 585 6 re /R7 9.98532 Tf 837 1039.67 l 1 0 0 1 240.72 677.72 Tm der y-Achse. ( )Tj 1481 4164.67 l [( )-2.33512(t)1.634( )-2.33512(z)-0.589648(u)7.3486( )-2.33512(P)-8.74791(\()-3.44695(2)-4.66731(t)278]TJ (2)Tj [( )-9766.66(l)2.42207(\))-2.48609( )-552.77(f)]TJ (1)Tj 23.28 0 Td 2926 2384.67 m /R7 9.96 Tf (2)Tj /R7 9.98676 Tf 2.52 0 Td Ausführliche Lösung Der Koordinatenursprung wird in die linke untere Ecke des Torbogens gelegt. [( )-2.33439(6)-4.66805(x)500]TJ /R7 9.98532 Tf /R7 9.98676 Tf 1 0 0 1 332.88 288.2 Tm 1 0 0 1 121.2 234.32 Tm 7.92 0 Td 7.92 0 Td q 0.952057 0 0 -1.04794 0 0 cm [( )-2.37067(3)-4.74134( )-2.37067(u)7.27631(n)7.27631(d)-4.74134( )-2.37067(g)7.27631(\()-3.49439(x)7.27631(\))-3.49439( )-2.37067(=)-0.830321( )250]TJ 140.76 -1.56 Td ()Tj /R15 9.96 Tf 2189 3863.67 6 94 re /R7 6.48 Tf 3.24 -4.56 Td 1254 1251.67 m ()Tj W n 8.28 -6.36 Td Bestimme die ganzrationale Funktion 2. (2)Tj /D[1 q 83 0 0 30 0 0 cm f 8.33333 0 0 8.33333 0 0 cm BT 2744 1105.67 l 1182 4258.67 l q 989 1478.67 m /R7 6.48 Tf /R7 9.98676 Tf ( )Tj ()Tj Q der y-Achse. /R7 6.48 Tf 27.24 4.56 Td q /R7 10.0134 Tf d1) Bestimmen Sie die Zahl a so, dass die Funktion ga mit der Funktion f über-einstimmt. BI ( )Tj Übungsblatt 4499. ()Tj Five strategies to maximize your sales kickoff; Jan. 26, 2021. /R7 6.48 Tf T*[(A)-0.891628(u)1.78326(f)-4.34967(g)-6.0241(a)-6.0241(b)1.78326(e)-1.78326( )-3.01208(1)-6.0241(2)-6.0241(:)-4.34967( )-3.01205(B)-7.69852(e)-1.78326(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(v)-6.0241(o)-6.0241(n)1.78252( )-3.01205(F)-3.45768(u)1.78252(n)1.78252(k)13.8307(t)-4.34894(i)0.89126(o)-6.02263(n)1.78252(s)3.45768(g)-6.0241(l)0.89126(e)-1.78252(i)0.89126(c)-1.78252(h)1.78252(u)1.78252(n)1.78252(g)-6.0241(e)-1.78252(n)1.78306( )]TJ /IM true /R15 9.96 Tf <> <> /R15 9.96 Tf f /R7 6.48 Tf f (t)Tj [( )250]TJ f 8.33333 0 0 8.33333 0 0 cm BT 4.128 w /R7 10.0134 Tf /R7 6.48 Tf 3 2.04 Td 1598 4157.67 6 6 re 2543 2938.67 6 94 re 2737 5946.67 m [(3 )250]TJ q -308.4 -19.44 Td 279.6 0 Td Klasse > Ganzrationale Funktionen > Anwendungsaufgaben. 7.44 4.56 Td 1 0 0 1 341.16 247.04 Tm [( )-2.00394(+ )-2.00394(2)-4.00788(x)500.008]TJ /R15 9.96 Tf 8.33333 0 0 8.33333 0 0 cm BT /R15 9.96 Tf 834 4151.67 m ( )Tj /R7 9.99984 Tf 8.33333 0 0 8.33333 0 0 cm BT (1)Tj /R15 9.96 Tf /R15 9.96 Tf /R7 9.98676 Tf ()Tj 2898 3863.67 6 94 re h 900 1039.67 l 3.24 -4.56 Td 3.72 0 Td (3)Tj (4)Tj 1 0 0 1 149.88 589.76 Tm 23.16 4.56 Td [(\()-3.44695(x)7.3486(\))-3.44695( )-2.33512(=)564]TJ /R7 10.0134 Tf /R7 9.98676 Tf 1 0 0 1 462.36 325.76 Tm /R7 10.0232 Tf [(1)7.34713(0)500]TJ ()Tj Realschulabschluss. endobj 39.72 0 Td /R7 9.98532 Tf ( )Tj 58.44 0 Td <> 2189 4894.67 6 6 re 45.6 0 0 0 48 31 d1 q f -350.64 -24.6 Td /R15 9.96 Tf /R8 9.96 Tf 7.92 0 Td /R15 9.96 Tf 8.4 0 Td 1.8 1.56 Td 67.08 4.56 Td /R7 9.98532 Tf (3)Tj (3)Tj /R15 9.96 Tf 1 0 0 1 402.6 256.64 Tm 1 0 0 1 100.44 240.44 Tm 7.92 0 Td Q S /R7 6.48 Tf 3247 4560.67 l (x)Tj Q Q /R7 9.99984 Tf -382.44 -12.36 Td f [(4 )250]TJ <> /R15 9.96 Tf <> [( )-3.01205(1)-6.0241(\))-4.34944( )-12231.9(h)6.0241(\))-4.34944( )-340.361(f)]TJ -424.8 -22.44 Td f 7.92 0 Td 2.52 0 Td f W n 74.88 0.12 Td 1 0 0 1 431.52 372.92 Tm 2259 5959.67 m f [( )-2.00394(= )250]TJ [( )-2.00394(+ )-2.00394(x)7.99232( )250]TJ 2.52 0 Td -0.12 14.28 Td 1 0 0 1 371.4 385.28 Tm Q /R7 9.99984 Tf q 0.952057 0 0 -1.04794 0 0 cm ()Tj 7.92 0 Td (4)Tj 3.24 -4.56 Td 2933 2280.67 l ( )Tj 7.92 0 Td q 3.24 -4.56 Td ET /R7 9.975 Tf [( )-2.00394(1)-4.00788(9)-4.00788(x)500.008]TJ (t)Tj /R7 6.48 Tf 4.92 -4.56 Td 2890 2026.67 l 1 0 0 1 92.88 322.04 Tm 9.36 -7.32 Td /R7 9.98676 Tf /R7 6.48 Tf 2673 1701.67 m 4141.56 -4352.02 m /R15 9.96 Tf 7.92 0 Td ( )Tj Prüfungsvorbereitung Lineare Funktionen /D[1 8.4 0 Td 2733 2372.67 l 2189 3232.67 6 6 re 7.92 0 Td 3744 3082.67 m ()Tj 2.52 0 Td 1 0 0 1 299.64 377.48 Tm anger management coloring sheets for kids ..., image source: i1.rgstatic.net. ET 1 0 0 1 326.16 565.04 Tm [( )-2.33366(+)-0.748061( )-2.33366(2)-4.66878(2)-4.66878(x)7.34713( )250]TJ h ET (3)Tj ET 2.52 0 Td Q [( )-3.01205(1)-6.0241(\))-4.34944( )-12231.9(k)6.0241(\))-4.34944( )-340.361(f)]TJ /R15 9.96 Tf 1 0 0 1 102.24 385.28 Tm /R15 9.96 Tf 3.24 -4.56 Td 1 0 0 1 480.24 455.96 Tm ()Tj 1348 5944.67 m 7.8 0 Td 1.8 1.56 Td 1 0 0 1 153.36 229.76 Tm /R7 6.48 Tf [(d)-3.3255(\))-2.5504( )-325.229(f)9.4334(\()-2.55054(x)8.65808( )-1.66257(+)0.754848( )-1.66257(2)-3.32587(\))-2.55054( )250]TJ 3895 4608.67 l Q 7.92 0 Td 8.28 -7.32 Td 12.48 4.56 Td -311.28 -12.36 Td 2733 2396.67 l -365.28 -12.36 Td /R7 9.99984 Tf 2979 2159.67 l 384 3238.67 6 225 re 3.24 -4.56 Td /R7 9.96 Tf 1 0 0 1 458.64 390.32 Tm S [(e)-0.588548(\))-3.44553( )-386.843(f)8.57043(\()-3.44548(x)7.34787(\))-3.44548( )-2.33439(=)-0.748061( )250]TJ Ausführliche Lösung Das Gleichungssystem: Der Gauß- Algorithmus: Die Koeffizienten und die Funktionsgleichung: Q 2665 3083.67 m Nun werden ganzrationale Funktionen höheren Grades, also mit Potenzen, in denen die Exponenten größer als zwei sind, untersucht. (PDF) An evaluation of a brief anger management programme ..., image source: www.therapistaid.com. /R15 9.96 Tf 3785 3326.67 l /F/CCF 1232 5734.67 l (l)Tj 2898 2738.67 6 94 re [( )-2.37067(f)8.52326(�)7.27631(r)-3.49439( )-2.37067(t)1.59316( )250]TJ ( )Tj /R15 9.96 Tf ( )Tj /R7 10.0134 Tf /R7 9.99984 Tf /R11 1 Tf 7.92 0 Td 19.08 4.56 Td q ( )Tj ET [(c)-0.588548(\))-3.44553( )-386.843(2)-4.66805(x)500]TJ [(\))-3.84164(\()-3.84164(x)6.76692( )-2.63158(+)-1.41418( )250]TJ [(t)805.294(2)]TJ 3.24 -4.56 Td 3859 4187.67 l 7.92 0 Td (2)Tj /R7 6.48 Tf /R15 9.96 Tf 1 0 0 1 391.2 288.2 Tm /R7 6.48 Tf 47.28 0 Td 1 0 0 1 329.04 397.64 Tm /R7 9.98676 Tf /R7 9.98676 Tf f q q 1 0 0 1 93 166.76 Tm [(\()-3.44695(x)7.3486(\))-3.44695( )-2.33512(=)-0.748061( )-2.33512(x)500]TJ /R7 6.48 Tf 2549 2732.67 349 6 re 128.16 -0.12 Td [( )-2.33439(3)-4.66805(x)500]TJ Klausurvorbereitung - Analysis - NRW. 2920 2041.67 m (r)Tj 4.128 w 2645 4464.67 m 18.96 -1.56 Td h ()Tj [(3)-4.66878(\))-3.44548( )-7812.68(j)-10.3819(\))-3.44696( )-543.051(f)]TJ (x)Tj ()Tj 0.12 0 0 -0.12 153.48 614.52 Tm (2)Tj 1 0 0 1 149.04 564.56 Tm /H 30 /R7 10.0134 Tf /R7 9.96 Tf Jan. 26, 2021. S 390 2632.67 618 6 re 1 0 0 1 153 112.88 Tm S W n /R7 9.975 Tf 2.52 0 Td /R7 9.98676 Tf f 8.33333 0 0 8.33333 0 0 cm BT /R7 6.48 Tf [( )-2.00394(1)-4.00788(0)-4.00788(\))-3.00539( )]TJ /R15 9.96 Tf 390 3232.67 618 6 re 3522 4258.67 l /R7 9.99984 Tf /R15 9.96 Tf /R7 10.0232 Tf 3.24 -4.56 Td 2.52 0 Td 77.64 -1.56 Td 11.16 TL [(9)-5.26316(6)-5.26316(\))-3.84214( )]TJ ET Blog. [(\()-3.44695(x)7.3486(\))-3.44695( )-2.33512(=)-0.748061( )-2.33512(t)1.634(x)500]TJ Q 12.48 4.56 Td 8.33333 0 0 8.33333 0 0 cm BT /R7 6.48 Tf f /R8 14.04 Tf [( )-2.63158(8)-5.26316( )-2.63158(=)-1.41418( )-2.63158(\()-3.84164(x)6.76692( )-2.6316(+)-1.41418( )-2.63158(4)-5.26316(\))-3.84164(\()-3.84164(x)6.76692( )-2.6316(+)-1.41271( )-2.63158(2)-5.26316(\))-3.84164(\()-3.84164(x)6.76692( )250]TJ ()Tj ()Tj f q 0.12 0 0 -0.12 462.6 478.08 Tm /R15 9.96 Tf ( )Tj 2898 3857.67 6 6 re S f 4.92 -4.56 Td /R7 6.48 Tf 2898 4794.67 6 6 re ()Tj 2.52 0 Td 3296 4258.67 m 3.24 -4.56 Td /R7 9.975 Tf S 8.33333 0 0 8.33333 0 0 cm BT 2.52 0 Td /R7 6.48 Tf %���� /R22 9.98532 Tf 1 0 0 1 153.12 127.16 Tm [(\()-3.44695(1)500]TJ -375 -11.28 Td 5.04 0 Td /R15 9.96 Tf /R7 9.96 Tf 1 0 0 1 95.16 479.12 Tm 1671 1455.67 l 3001 2265.67 l /R7 9.96 Tf ()Tj /R7 9.975 Tf f 33.12 0 Td (2)Tj [( )-2.33512(+)-0.748061( )-2.33512(b)-4.66731(x)7.3486( )-2.33512(+)-0.748061( )-2.33512(c)-0.588731( )]TJ W n 2.52 2.04 Td [( )-6859.77(0)-5.26316(,)-2.63158(2)-5.26316(5)-5.26316(4)-5.26316(8)-5.26316(7)-5.26316(5)-5.26321( )-3058.27( )-4020.68( )]TJ 4390 3235.67 l [( )-2.00394(6)-4.00788(\))-3.00591( )-2.00394(:)1.99515( )-2.00394(\()-3.00591(x)7.99232( )-2.00394(+ )-2.00394(2)-4.00788(\))-3.00539( )]TJ /R7 9.975 Tf 96.24 4.56 Td Q [( )-2.33366(4)-4.66878(x)500]TJ ()Tj <> f /R15 9.96 Tf 1.8 1.56 Td -59.64 -11.28 Td /R7 6.48 Tf /R7 9.98532 Tf (2)Tj 2543 4457.67 6 6 re 390 3857.67 618 6 re Lerninhalte zum Thema Ganzrationale Funktionen findest du auf dem Lernportal Duden Learnattack.. Mit Duden Learnattack bereiten sich Schüler optimal auf Mathematik Klassenarbeiten vor.. Interessante Lerninhalte für die 10.Klasse: Verständliche Lernvideos Interaktive Aufgaben Original-Klassenarbeiten und Prüfungen Musterlösungen 2.52 0 Td ()Tj /R7 9.98532 Tf [( )-2.33439(6)-4.66805(x)7.34713( )-2.33366(+)-0.748061( )-2.33366(4)-4.66829( )-13316(f)8.56896(\))-3.44696( )-507.003(f)]TJ 1 0 0 1 156.24 443.6 Tm [(6 )250]TJ 1008 4157.67 6 6 re /R7 9.98676 Tf (2)Tj /R8 9.96 Tf /R11 1 Tf 7.8 0 Td 17.4 -1.56 Td q (x)Tj 0.12 0 0 -0.12 95.64 148.92 Tm /R7 9.96 Tf /R7 9.96 Tf Bei ganzrationale Funktionen: Es kommen nur Summanden mit geraden Exponenten vor. ()Tj 4530 559.668 m [( )-3.01205(2)-6.0241(x)500]TJ 1 0 0 1 448.56 455.96 Tm 2549 4457.67 349 6 re [( )-2.00394({)479.999]TJ [(N)1.98856(u)7.99232(l)1.99588(l)1.99588(s)4.99373(t)1.99588(el)1.99588(l)1.99588(en)7.99232( )-2.00394(au)7.99232(f)8.99502(w)25.9897(ei)1.99515(s)4.99373(en)7.99232( )-2.00394(u)7.99232(n)7.99232(d)-4.00788( )-2.00394(au)7.99232(�)-4.00788(er)-3.00591(d)-4.00788(em)21.9877( )-2.00394(d)-4.00788(u)7.99232(r)-3.00591(ch)7.99232( )-2.00394(d)-4.00788(en)7.99232( )-2.00394(P)-8.00989(u)7.99232(n)7.99232(k)7.99232(t)1.99515( )-2.00404(P)-8.00989( )-2.00394(v)7.99232(er)-3.00591(l)1.99515(au)7.99232(f)8.99428(en)7.99232(:)1.99557( )]TJ 7.92 0 Td ( )Tj Q /R7 9.98676 Tf 2924 4151.67 m /R7 6.48 Tf 0 g 1 0 0 1 351.96 248.84 Tm 1 0 0 1 530.4 549.32 Tm q 3.24 1.56 Td /R7 6.48 Tf (3)Tj 3.24 -4.56 Td 8.33333 0 0 8.33333 0 0 cm BT 1481 4045.67 l 1.8 1.56 Td /R8 9.96 Tf /R15 9.96 Tf Q 8.28 -7.32 Td ET /R7 9.98676 Tf h 2543 4363.67 6 94 re (2)Tj /R7 9.99984 Tf (2)Tj S 3.72 0 Td 1 0 0 1 436.2 468.32 Tm /R7 6.48 Tf 7.8 0 Td 47 0 obj /R7 9.96 Tf 1349 3238.67 l BI 16.92 4.56 Td Q 1 0 0 1 50.4 501.92 Tm [( )-2.00394(1)-4.00788(\))-3.00539( )-10034.2(f)8.99428(\))-3.00539( )-506.012(\()-3.00591(x)500.008]TJ q /R7 9.98532 Tf (t)Tj 1186 5721.67 m ( )Tj /R15 9.96 Tf 1 0 0 1 126.6 193.28 Tm /R7 6.48 Tf /R7 9.975 Tf /R7 6.48 Tf ET /R7 6.48 Tf h ( )Tj h /R7 6.48 Tf ()Tj ( )Tj 1228 5630.67 l h /R15 9.96 Tf ()Tj W n 4496 4018.67 m 3.24 -4.56 Td 0.12 0 0 -0.12 121.32 602.16 Tm 4.92 -4.56 Td 1289 3410.67 m 1 0 0 1 100.92 609.8 Tm f (2)Tj 7.92 0 Td ( )Tj (3)Tj endobj (x)Tj 2.52 0 Td ()Tj /R7 6.48 Tf W n /R7 9.98532 Tf 390 4557.67 618 6 re 2779 5855.67 l 1 0 0 1 124.08 442.04 Tm 3.24 1.56 Td ( )Tj 220.8 0 Td 7.92 0 Td 5.04 0 Td Q /R7 9.98676 Tf (1)Tj q 0.12 0 0 -0.12 472.44 745.08 Tm 8.33333 0 0 8.33333 0 0 cm BT /R7 10.0134 Tf /R15 9.96 Tf /R7 9.98676 Tf 38.16 0 Td /R7 9.96 Tf /R7 9.98676 Tf 1377 4164.67 l /R7 9.975 Tf 1 0 0 1 487.2 551.72 Tm (2)Tj ()Tj /R7 9.96 Tf [(1)-6.0241(,)-3.01205(8)-6.0241(5)-6.0241(6)-6.0241(2)-6.0241(5)-6.02416( )-3978.92(1)-6.0241(,)-3.01205(8)-6.0241(5)-6.0241(9)-6.0241(3)-6.0241(7)-6.0241(5)-6.02416( )]TJ -289.68 -12.36 Td 4390 3326.67 m 11.64 0 Td [( )-3.01205(2)-6.0241(\))-4.35041(\()-4.35041(x)6.0241( )-3.01205(+)-2.26492( )-3.01205(2)-6.0241(\))-4.35041( )-3.01205(f)7.69778(�)6.0241(r)-4.35041( )-3.01205(t)0.89126( )250]TJ Willkommen bei der Mathelounge! S [( )-2.37067(+)-0.829587( )-2.37067(8)-4.74134(x)500]TJ 7.92 0 Td
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