Question

How do you find the asymptotes for `R(x)=(3x+5) /(x-6)`?

Answer 1

vertical asymptote at x = 6 and a horizontal asymptote at y = 3

Explanation:

Vertical asymptotes occur when the denominator of the
rational function is 0.

In this question this would occur when x - 6 = 0 ie x = 6

[ Horizontal asymptotes can be found when the degree of the

numerator and the degree of the denominator are equal. ]

Here they are both of degree 1 and so are equal.

The horizontal asymptote is found by taking the ratio of leading

coefficients .

hence y`=3/1 = 3`
graph{(3x+5)/(x-6) [-40, 40, -20, 20]}