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Given the function h of x equals negative 2 times the square root of x, which statement is true about h(x)?

The function is decreasing on the interval (0, ∞).
The function is decreasing on the interval (–∞, 0).
The function is increasing on the interval (0, ∞).
The function is increasing on the interval (–∞, 0).

Respuesta :

Using translation concepts, it is found that the correct statement about h(x) is:

The function is decreasing on the interval (0, ∞).

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 parent function is:

[tex]f(x) = \sqrt{x}[/tex]

Which is increasing on (0, ∞).

After the translation, the function is:

[tex]h(x) = -2\sqrt{x}[/tex]

It was multiplied by a negative number, which means that it was reflected over the x-axis, and it will be decreasing on the interval (0, ∞).

More can be learned about translation concepts at https://brainly.com/question/4521517

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