# How do you graph #f(x)=(x^2-16)/(x^2-6x+8)# using holes, vertical and horizontal asymptotes, x and y intercepts?

##### 1 Answer

First, factor:

As you can see, there is

To find the vertical asymptote, set the simplest form of the denominator equal to zero:

So set

To find a horizontal asymptote, find the degree the polynomials are. Let's say

If

If

If

Here, the degrees are the same so

(

To find the x-intercept, plug in

The x-intercept is at

To find the y-intercept, plug in

The y-intercept is at

Graph it:

graph{(x^2-16)/(x^2-6x+8) [-15.26, 17.28, -6.31, 9.96]}