SOLUTION: What is the equation of the vertical asymptote and horizontal asymptote of the rational function: f(x) = 8x^2+2x-3/ x^2-4x

Algebra ->  Functions -> SOLUTION: What is the equation of the vertical asymptote and horizontal asymptote of the rational function: f(x) = 8x^2+2x-3/ x^2-4x       Log On


   

Question 846777: What is the equation of the vertical asymptote and horizontal asymptote of the rational function:
f(x) = 8x^2+2x-3/ x^2-4x
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=%28+8x%5E2%2B2x-3%29%2F+%28x%5E2-4x%29
f%28x%29=%28%282x-1%29%284x%2B3%29%29%2F%28x%28x-4%29%29
Vertical asymptotes occur when denominator goes to zero.
x%28x-4%29=0
Two solutions:
x=0
and
x-4=0
x=4
Horizontal asymptote : Divide numerator and denominator by x%5E2 and take the limit as x-%3Einfinity

There is a horizontal asymptote at y=8