Question

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

Answer 1

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 = `4/1 =4`
graph{(4x+8)/(x-3) [-40, 40, -20, 20]}