# What is the range of #f(x)=–5-2(x+3)^2#?

##### 1 Answer

The range is

#### Explanation:

The **range** of a function is simply all the possible outputs that function can give.

Mathematically speaking, a number

There are a couple of ways to find the range of a function. For *parabolic function*. As such, there is no limitation on the *domain* is

Take a look at that squared bit—the

So *no more than* 0, and thus

In math:

#color(white)(f(x)="-5"-2)(x+3)^2>=0#

#color(white)(f(x)="-5"-)2(x+3)^2>=0#

#color(white)(f(x)="-5")-2(x+3)^2<=0" "# (note the change to#<=# )

#f(x)="-5"-2(x+3)^2<="-5"#

The end result:

And so our range is "all numbers

#{y|y<="-5"}# .

## Bonus:

The shortcut to finding the range of a parabolic equation

Range of

#f(x)# is#{({y|y>=k}" when "a>0),({y|y<=k}" when "a<0):}#

Just choose the correct option depending on the value of