Question

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

Answer 1

Using translation concepts, it is found that the correct statements are given as follows:

• 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).

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the functions are:

• g(x) = x².

• h(x) = -x².

h(x) = -x² = -g(x), which means that h(x) is a reflection of g(x) over the x-axis. Since $g(x) \geq 0$ for all values of x, $h(x) \leq 0$ for all values of x, which means that they are equal at the origin and g is greater for other values of x, hence the correct statements are:

• 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).

More can be learned about translation concepts at brainly.com/question/4521517

#SPJ1