Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? check all that apply. for any value of x, g(x) will always be greater than h(x). for any value 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

g(x) > h(x) for x = -1 is TRUE

For positive values of x, g(x) > h(x) is TRUE

For negative values of x, g(x) > h(x) is also TRUE

EXPLANATION

The given functions are

and

If

Based on this options A and B are FALSE.

When

for x=-1 is True.

When x=3,

and

g(x) < h(x) for x = 3 is a FALSE statement.

For positive values of x, g(x) > h(x) is TRUE

See graph.

For negative values of x, g(x) > h(x) is also TRUE

See graph