given f(x)=10-x^2, what is the range?

Question

I need to know the range of the problem f(x)=10-x^2 for my precalculus test.

Answer 1

I need to know the range of the problem f(x) = 10 - x^2 for my precalculus test.

x^2 is always positive.

So -x^2 is always negative.

That means that 10 - x^2 is negative for large values of x.

10 - x^2 is only positive for x smaller than sqrt(10), and has its greatest positive value when x = 0.

That greatest value is f(0) = 10.

The range of the function then is from minus infinity to plus 10.

Range = (-ꝏ, 10]