How do you find the horizontal and vertical asymptote for this rational function.

Question

This question is a test for supplying a link to a Desmos graph.

How do you find the horizontal and vertical asymptotes for this rational function?

f(x) = (3x)/(x-2)

Answer 1

f(x) = 3x/(x-2) has a vertical asymptote of x=2 and a horizontal asymptote of y= 3

whatever value makes the denominator = 0 is a vertical asymptote: set the denominator = 0 and solve for x

for the vertical asymptote look at the ratio of the highest powered terms in the numerator and denominator: 3x/x = 3. ignore the other terms, if any. y=3 is a line that the graph approaches as x gets very large or very small.