Answered

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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).

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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