Question

What is the range of the function `f(x)= -x^2 +9`?

Answer 1

Range of `f(x) = [9, -oo)`

Explanation:

`f(x) = -x^2+9`

`f(x)` is defined `forall x in RR`

Hence, the domain of `f(x) = (-oo, +oo)`

Since the coefficient of `x^2 <0` `f(x)` has maximum value.

`f_max = f(0) = 9`

Also, `f(x)` has no lower bounds.

Hence, the range of `f(x) = [9, -oo)`

We can see the range from the graph of `f(x)` below.

graph{-x^2 +9 [-28.87, 28.87, -14.43, 14.45]}