# How do you find the domain and range of #f(x) =x^2+8x+15#?

##### 1 Answer

Domain:

Range:

#### Explanation:

Given:

#f(x) = x^2+8x+15#

First note that in common with any polynomial, the (implicit) domain of

We can find the range by completing the square:

#x^2+8x+15 = x^2+8x+16-1 = (x+4)^2-1#

Note that

Then since

So the range is

Another way of finding the range is to set

Given:

#y = x^2+8x+15 = (x+4)^2-1#

Add

#y + 1 = (x+4)^2#

Take the square root of both sides, allowing for both possibilities to get:

#x+4 = +-sqrt(y+1)#

Subtract

#x = -4+-sqrt(y+1)#

So for any