# How do you graph #f(x)=x^2/(x-4)# using holes, vertical and horizontal asymptotes, x and y intercepts?

##### 1 Answer

No holes, one VA at

#### Explanation:

A vertical asymptote occurs in a rational function when there is

If we set the denominator equal to

Now we know that the function has a vertical asymptote at

We also know that there are no holes in the function because holes occur when there are factors in common in the numerator and the denominator; this function doesn't have any common factors.

An

There's an

Lastly, find the EBA (end behavior asymptote). Since the power in the numerator is greater than the power in the denominator, we have to divide the two using synthetic division:

The quotient is

The final graph looks like this:

graph{x^2/(x-4) [-47.03, 56.97, -18.04, 34]}

As you can see, there are no holes, 1