Write a rational function f that has the specified characteristics. (There are many correct answers.)   a) vertical asymptote: x=5 horizontal asymptote: y=0 zero: x=1 f(x)= ______   b) vertical asymptote: x=-5 horizontal asymptote: y=0 zero: x=5 f(x)= ______   c) vertical asymptote: x=-5, x=5 horizontal asymptote: y=4 zero: x=4, x=-4 f(x)= ______

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 53E
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Write a rational function f that has the specified characteristics. (There are many correct answers.)

 

a) vertical asymptote: x=5

horizontal asymptote: y=0

zero: x=1

f(x)= ______

 

b) vertical asymptote: x=-5

horizontal asymptote: y=0

zero: x=5

f(x)= ______

 

c) vertical asymptote: x=-5, x=5

horizontal asymptote: y=4

zero: x=4, x=-4

f(x)= ______

 

d) vertical asymptote: x=-4, x=3

horizontal asymptote: y=-4

zero: x=-3, x=5

f(x)= ______

 

e) vertical asymptote: x=0, x=±3

horizontal asymptote: y=-3

zero: x=-1, x=1, x=2

f(x)= ______

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