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Sagot :
Using translation concepts, it is found that the correct statements are given as follows:
- 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).
What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the functions are:
- g(x) = x².
- h(x) = -x².
h(x) = -x² = -g(x), which means that h(x) is a reflection of g(x) over the x-axis. Since [tex]g(x) \geq 0[/tex] for all values of x, [tex]h(x) \leq 0[/tex] for all values of x, which means that they are equal at the origin and g is greater for other values of x, hence the correct statements are:
- 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).
More can be learned about translation concepts at https://brainly.com/question/4521517
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