# How do you graph #f(x)=(x^2-5x+6)/(x^2-4x+3)# using holes, vertical and horizontal asymptotes, x and y intercepts?

##### 2 Answers

See below.

#### Explanation:

It would be very hard to graph this equation correctly as without factoring both the numerator and denominator it would be hard to account for all of the information.

Then, following the same process for the bottom, you get

Based on this, you can rewrite f(x) as:

Now you are ready to graph with all of the criteria. Since

Vertical asympotes can be found in the denominator, just set

For the horizontal asymptote, in this case, you would take the ratio of the leading coefficients of the numerator and denominator. Since this is

Zeros are found in the top. You set

You know the

That's all. Hope that helps!

See graph

#### Explanation:

In addition to to the answer below, here is what the graph would look like. Keep in mind however, that this graph show the "hole" at

graph{(x^2-5x+6)/(x^2-4x+3) [-10, 10, -5, 5]}