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# Week 10 Notes 126B

WVU

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This 6 page Class Notes was uploaded by Thomas Frerks on Monday October 26, 2015. The Class Notes belongs to 126B at West Virginia University taught by ***** *****STAFF***** (P) in Fall 2015. Since its upload, it has received 14 views. For similar materials see College Algebra 4-Day in Mathematics (M) at West Virginia University.

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Date Created: 10/26/15

Unit 4 Rational Functions and Exponential Functions Section 15 I Basics of Rational Functions 0 De nition A Etional function is a ratio of two where the ma f YpQ m 39 Z is nonzero In other words a rational ftmction is a function of the form x Rx Q Ci where X and ZCX are polynomials with nonzero Examples Write some examples of rational Functions 6 00 in f ltXSfX lffx y C K 0041 x39 0 Example Look at the examples you wrote above What are the domains of these functions I XXi 0H 5 0 3 XX 0 xf 4 r M 0 Example Let Rx What is the domain of Rx39 0 gt6 I X 02 WW km 2 x 93100 x4 X t Jarxzat 0 De nition A rational tnction is groper if 0f I74 Unit 4 Rational Functions and Exponential Functions Section I 5 2 Vertical Asyngptotes of Rational Functions 0 Example Consider the reciprocal function Rx 1 Make a chart of x the values of Rx for xvalues 2 1 12 U3 U4 and 15 Next make a chart of the values of Rx for xvalues 2 1 12 1X3 l4 and 15 x x Rx x Rx X 2 101 2 72 1 1 1 1 12 01 42 32 13 3 13 a 14 L7 14 L US 5 l5 5 0 00 oo 0 0 Example What is happening to the values of Rx as values of x get closer and closer to zero 71c 55 c339 r end layff in mafmyvce 0 Example For Rx 1 as the xvalues approach 0 the y values I 2 If a tiger bccomc U jot ea C 2 gavecquot A t M r MCI 0 De nition A rational function Rx has a vertical asymptote at x r if as the xvalues approach f the yvalues become Maison64 I r quot 00 W 00 176 Unit 4 Rational Functions and Exponential Functions 0 Other examgles and nores X 1 X Wow xii204 xw H U d 0 I 3 XX JXJ 9 X 393 quot l tht r a afw bfc39r XampX j R my Uri Um X27 X I 3912 5 Afry YI armJoz e 178 Unit 4 Rational Functions and Exponential Functions 0 Example Can the graph of a rational mction intersect its horizontal asymptote 0 Example How many horizontal asymptotes can a rational function have 37 Glee5 Come None Or one E c UI Of 0 Example Write some examples of rational functions that have horizontal asymptotcs 39 1 JX rm 2 I Am 1 a 509 4 X 93 WW1 405 7 YJZO 530 gal o g nition If an asymptote is neither vertical nor horizontal it is called 0 05 Age or s f nCC Oblique asymptotes also have to do with the e 94 b66tamp439Q of a function 0 What is an example of a function with an oblique asymptote L 1 Lon A00 5 x V V X 73 Dev3km xhx w Example Can a graph intersect its oblique asymptote 180 Unit 4 Rational Functions and Exponential I unctions 3 The degree of px is one more than the degree of qx 2 an 2 X X3 agree 2 39 dwzr ran f f X 1 1 6 ay66 av l rm m 6 j z X Ski x fox fox J DA ve J7lt 3 bx 26 fx H e I i ri e 4 The degree of px is greater than the degree of qx by two or more M Aari39zmG 0r 0 de 2 00 051 x 06369 5 L1 X J Loaf AzJ a 7 ne 50 10 hanW 0r a rque asympoj 0 coating Horizontal and Obligue Asymptotgs Let Q px auxquot am a and qx bmxm l but bf be two nonzero polynomials Fill in this chart about nding the Pix horizontal or oblique asymptotcs of the rational function Rx q x 182 Unit 4 Rational Functions and Exponentian Functions 0 39xample Find the horizontal or oblique asymptotes if any of the graph of 4x 1m 2x 1 21 Del 1 39 0 AOrI Zma 0 Example Find the horizontal or oblique asymptotcs if any of the graph 58 4x 1 l 738 2x I 5 iii ef Dot 9A 77 Awnam al 0 Example Find the horizontal or oblique asymptotes if any of the graph of2x3 5x24x lx22x l 051409 c X9 l X Xjfxlcfy aiiii if 9x x 4 ampx iZOLX Q 051406 l 184

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