# How do I find the range of the function f(x)=10-x^2?

Sep 26, 2014

The range of $f$ is $\left(- \infty , 10\right]$.

Let us look at some details.

Since ${x}^{2} \ge 0$,

$f \left(x\right) = 10 - {x}^{2} \le 10 - 0 = 10$,

so the largest value of $f$ is $10$.

Since ${x}^{2}$ can be made as large as we wish by choosing large, $f \left(x\right) = 10 - {x}^{2}$ can be made as small as we wish, which can be represented by $- \infty$.

Hence, the range is $\left(- \infty , 10\right]$.

The graph of $f$ looks like this:

I hope that this was helpful.