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Given h of x equals 3 times the square root of x plus 2 end root, which of the following statements describes h(x)?

The function h(x) is increasing on the interval (–∞, –2).
The function h(x) is decreasing on the interval (2, ∞).
The function h(x) is decreasing on the interval (–∞, 2).
The function h(x) is increasing on the interval (–2, ∞).

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Answer:

The function h(x) is increasing on the interval (-2, ∞)

Step-by-step explanation:

Given function:  [tex]h(x)=3 \sqrt{x+2}[/tex]

We cannot square root a negative number, therefore the domain (x-values) is restricted:

[tex]x+2\geq 0 \implies x\geq -2[/tex]

Therefore, [tex]h(x)\geq 0[/tex]

⇒ The function h(x) is increasing on the interval (-2, ∞)

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