# How do you graph #y=1/(x^2-x-6)#?

##### 1 Answer

You find the intercepts and the asymptotes, and then you sketch the graph.

#### Explanation:

**Step 1. ** Find the

Set

The

**Step 2.** Find the

Set

This is an impossibility, so there is no

**Step 3.** Find the vertical asymptotes.

Set the denominator equal to zero and solve for

There are vertical asymptotes at

**Step 4.** Find the horizontal asymptote.

The degree of the denominator is less than the degree of the numerator, so

The horizontal asymptote is at

**Step 5.** Draw your axes and the asymptotes.

**Step 6.** Sketch the graph in each region defined by the asymptotes.

**(a)** The **left hand region** has the

The point at (

**(b)** The **right hand region** has

The point at (

So we have a mirror-image hyperbola in the first quadrant.

**(c)** In the **middle region**, we have

The points at (