# What is the domain and range of # f(x) = (x+3) /( x^2 + 8x + 15)#?

##### 2 Answers

The domain is

#### Explanation:

The function is

The denominator must be

Therefore,

The domain is

To calculate the range, let

The denominator must be

The range is

graph{1/(x+5) [-16.14, 9.17, -6.22, 6.44]}

Domain:

Range:

#### Explanation:

We can factor the denominator as

We can cancel out common factors to get

The only value that will make our function undefined is if the denominator is zero. We can set it equal to zero to get

Therefore, we can say the domain is

To think about our range, let's go back to our original function

Let's think about the horizontal asymptote. Since we have a higher degree on the bottom, we know we have a HA at

graph{(x+3)/((x+3)(x+8)) [-17.87, 2.13, -4.76, 5.24]}

Notice, our graph never touches the

We can say our range is

Hope this helps!