# What is the domain and range of #f(x) = (10x)/(x(x^2-7))#?

##### 1 Answer

Domain:

Range:

#### Explanation:

First, simplify your function to get

The *domain* of the function will be affected by the fact that the denominator **cannot be zero**.

The two values that will cause the denominator of the function to be

zero are

This means that the domain of the function cannot include these two values,

The range of the function will also be affected by the domain restriction. Basically, the graph will have **two vertical asymptotes** at

For values of *maximum* for

This means that the range of the function will be

graph{10/(x^2-7) [-10, 10, -5, 5]}