Question

Graph all vertical and horizontal asymptotes of the function.
f(x)=(-8x+7)/(-2x+9)
My main question is how do I figure out how to get the vertical and horizontal asymptotes? I can graph once I figure that out.

Answer 1

Degrees of numerator and denominator are equal. So to find the horizontal asymptote, divide the coefficient of the x term in the numerator by the coefficient of the x term in the denominator. So the horizontal asymptote is:
\[y=\frac{-8}{-2}=4\]

Answer 2

To find the vertical asymptote set the denominator equal to 0 and solve.:
\[-2x+9=0\]
\[x=\frac{9}{2}\]