Question

How do you find vertical, horizontal and oblique asymptotes for `f(x)=(3x)/(x-8)`?

Answer 1

The vertical asymptote is `x=8`
The horizontal asymptote is `y=3`
There is no oblique asymptote

Explanation:

As you cannot divide by `0`, so `x!=8`
Therefore the vertical asymptote is `x=8`

As the degree of the numerator is equal to the degree of the denominator, there is no oblique asymptote.

Limit `f(x)=(3x)/x=3`
`x->+-oo`
Therefore `y=3` is a horizontal asymptote

graph{3x/(x-8) [-65.8, 65.9, -32.9, 33]}