# What is the range of the function #f(x)=10-x^2#?

##### 1 Answer

#### Explanation:

The *range of a function* represents all the possible output values that you can get by plugging in all the possible *domain*.

In this case, you have no restriction on the domain of the function, meaning that

Now, the square root of a number is **always** a positive number when working in **always** be positive.

#color(purple)(|bar(ul(color(white)(a/a)color(black)(x^2 >=0 color(white)(a)(AA) x in RR)color(white)(a/a)|)))#

This means that the term

#10 - x^2#

will **always** be smaller than or equal to

The range of the function will thus be

#color(green)(|bar(ul(color(white)(a/a)color(black)(y in (- oo, 10]color(white)(a/a)|)))#

graph{10 - x^2 [-10, 10, -15, 15]}