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

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Answer 1 · 2014-09-26T21:52:48

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

Let us look at some details.

Since $x^2 ge 0$ ,

$f(x)=10-x^2 le 10-0=10$ ,

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

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

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

The graph of $f$ looks like this:

enter image source here

I hope that this was helpful.

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