College Algebra
posted by Shasta on .
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(x17)^2/(x+12)^3

f(x) = x(x17)^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 
Want to let you know that the H.A. is WRONG by the way