Posted by **Shasta** on Tuesday, December 18, 2012 at 8:52pm.

Given the following rational functions,find:a.)the horizontal asymptote(s), b.)the vertical asymptote(s), if any,and c.) the oblique asymptote(),if any. f(x)=x(x-17)^2/(x+12)^3

- College Algebra -
**Reiny**, Tuesday, December 18, 2012 at 9:03pm
f(x) = x(x-17)^2 / (x+12)^3

a)

Horizontal as:

consider what happens when x becomes large

When expanded both numerators and denominators lead with +x^3

so as x ---> ∞ f(x) = x^3 .../x^3 ... = 1

e.g.

let x = 100,000 , f(100,000) = .9993..

let x = -100,000 , f(-100,000) = 1.0007...

so the H.A. is y = 1

b)

vertical asymptotes are caused by the denominator becoming zero

x+12=0

x = -12 is your V.A.

c) no oblique

- College Algebra -
**South university**, Friday, April 12, 2013 at 10:34pm
Want to let you know that the H.A. is WRONG by the way

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