Question

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, ∞).

Answer 1

Answer:

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

Step-by-step explanation:

Given function:  $h(x)=3 \sqrt{x+2}$

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

$x+2\geq 0 \implies x\geq -2$

Therefore, $h(x)\geq 0$

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