# How do you find the domain and range of #f(x)=(12x)/(x^2-36)#?

##### 2 Answers

Below

#### Explanation:

Looking at the graph, you can immediately see that there are 2 vertical asymptotes because

The horizontal asymptote is

Therefore, the graph cannot have the points with the y-coordinate

However, what asymptotes really tell you about the graph is that the end points of the graph will be approaching the horizontal and vertical asymptotes but they will never touch the asymptotes. Basically, it tells about the shape of the graph which can help you determine the domain and range of the graph.

Intercepts

When

When

You will notice that the graph can pass through

Hence,

Domain: all reals

Range: all reals

Below is the graph

graph{(12x)/(x^2-36) [-10, 10, -5, 5]}

The domain is

#### Explanation:

The denominator must be

Therefore,

The domain is

To find the range, let

This is a quadratic equation in

Therefore,

Therefore,

The range is

graph{12x/(x^2-36) [-32.49, 32.46, -16.24, 16.25]}