# What is the domain and range of #(x+3)/(x^2+9)#?

##### 2 Answers

#### Explanation:

The *domain* is the set of real values that

The *range* is the set of real values you can get out of the equation.

With fractions you often have to make sure that the denominator is not

Therefore, we know we can put pretty much anything into the equation.

The domain is

The range is found by recognising that

This means that the range is

The domain is

#### Explanation:

The domain is

For the range, proceed as follows,

Let

Then,

This is a quadratic equation in

In order for this equation to have solutions, the discriminant

Therefore,

Therefore,

The range is

You can cofirm this with a sign chart and a graph

graph{(x+3)/(x^2+9) [-7.9, 7.9, -3.95, 3.95]}