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

C,E and F on edge

Answer 2

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

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

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

Explanation:

We have the functions,
`g(x) = x^2` and
`h(x) = -x^2`.

From the graph plotted below, we see that,

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

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

Moreover, we have,

`g(x) = x^2`
`h(x) = -x^2`.

x= -1 g(x)= 1 h(x)= -1

x= 3 g(x)= 9 h(x)= -9

So, we get, g(x) > h(x) for x = -1 holds.

Thus, the options that are correct are 3, 5 and 6.