# How do you find the asymptotes for f(x)=(4x+8)/(x-3)?

Jan 22, 2016

vertical asymptote at x = 3 and a horizontal asymptote at y = 4

#### Explanation:

Vertical asymptotes occur when the denominator of the rational
function is 0.
here this would occur when: x - 3 = 0 ie x = 3

[Horizontal asymptotes can be found when the degree of the
numerator and the degree of the denominator are equal .]

In this question they are both of degree 1 and so equal.

and the asymptote is found by taking the ratio of leading >coefficients

hence y = $\frac{4}{1} = 4$
graph{(4x+8)/(x-3) [-40, 40, -20, 20]}