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).

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).

Step-by-step explanation:

Given functions: and

When x=0, and

∴ at x=0, g(x)=h(0)

Therefore the statements "For any value of x, g(x) will always be greater than h(x)." and "For any value of x, h(x) will always be greater than g(x)." are not true.

When x=-1, and

∴g(x) > h(x) for x = -1.  ......................(1)

When x=3, and

∴ g(x) > h(x) for x = 3....................(2)

⇒g(x) < h(x) for x = 3. is not true.

From (1) and (2),

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

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

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !