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

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

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

Step-by-step explanation:

For any value of x g(x) is always greater than h(x) and for any value of x, h(x) will always be greater than g(x) are not true.

The given function is:

g(x) = x^2 and h(x) = –x^2

x=0

g(0)=(0)^2 = 0

h(0)= -(0)^2 = 0

Now check the condition for x = -1

put x =-1 in the given functions.

g(x)=x^2

g(-1) = (-1)^2 = 1

h(x)= -x^2

h(-1) =  -(-1)^2 = -1

g(x)>h(x)

Now take a positive value of x= 3

Put the value in the given functions:

g(3) = (3)^2 = 9

h(3) = -(3)^2 = -9

g(x)>h(x)

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

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