Question

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

Answer 1

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

Answer 2

Want to let you know that the H.A. is WRONG by the way