Question

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 1

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

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

and

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

If

$x=0$

$g(0)={0}^{2}=0$

$h(0)=-({0})^{2}=0$

Based on this options A and B are FALSE.

When

$x=-1$

$g(-1)={( - 1)}^{2}=1$

$h(-1)=-{(-1)}^{2}=-1$

$g( - 1)>\:h(-1)$

for x=-1 is True.

When x=3,

$g(3)={3}^{2}=9$

and

$h(3)=-{3}^{2}=-9$

$g(3)>\: h( 3)$

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