Question

Which statements are true for the functions g(x) = x^2 and h(x) = –x^2 ? Check all that apply.A.For any value of x, g(x) will always be greater than h(x).B.For any value of x, h(x) will always be greater than g(x).C.g(x) > h(x) for x = -1. D.g(x) < h(x) for x = 3. E.For positive values of x, g(x) > h(x). F.For negative values of x, g(x) > h(x)

Answer 1

C, E, F

Explanation:

The range of the function
`g(x)=x^2` is
`y\in [0,\infty)`, the range of the function
`h(x)=-x^2` is
`(-\infty,0]`

This means that for any value of x, the value of
`g(x)` is always greater or equal to the value of
`h(x)` (the values are equal at x=0).

So, options A and B are false, because at x=0 the values are equal and h(x) cannot be greater than g(x)

Options C, E and F are true, because for all non-zero x, g(x)>h(x).

Option D is false (the reason is the same as for option B)