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

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

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Answer 1 · 2014-09-26T21:52:48

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

Let us look at some details.

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

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

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

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

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

The graph of $f$ $f$ looks like this:

enter image source here

I hope that this was helpful.

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

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