Question

Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.

For all non-zero values of x, g(x) will always be greater than h(x).
For all non-zero values of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).

Answer 1

True:
- For all non-zero values of x, g(x) will always be greater than h(x).
- g(x) > h(x) for x = -1.
- For positive values of x, g(x) > h(x).
- For negative values of x, g(x) > h(x).

Reason: g(x)=x^2 ≥ 0 and h(x)=−x^2 ≤ 0, with equality only at x=0. So for any nonzero x, x^2 > −x^2. The other two statements are false.