Question

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

Answer 1

HA at `y=3`
VA at `x=8`

Explanation:

For the horizontal asymptote, we want to compare the degrees of the numerator and denominator.

Comparing the degrees, we have

`(3x)/x`

We can cancel the variables to be left with a horizontal asymptote at `y=3`.

To think about the vertical asymptote, we want to think about what value makes our function undefined.

In our case, this function will be undefined when the denominator is equal to zero, and we see this happens at `x=8`.

With this in mind, we can say we have a vertical asymptote at `x=8`.

Hope this helps!