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

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.