Question

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

Answer 1

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. TRUE

g(x) < h(x) for x = 3.

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

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

Explanation:

answer on edge

Answer 2

See below

EXPLANATION

The given functions are:

`g(x) = {x}^(2)`

and

`h(x) = - {x}^(2)`

The following statements are true;

h(x) is the reflection of g(x) in the x-axis.

g(x) opens upwards while h(x) opens downwards

Both functions have their vertex and intercepts at the origin.

The x-axis is a tangent to both functions at x=0.

g(x) has a minimum point

h(x) has a maximum point.