Question

select the correct answer.
which statement is true about the function shown in the graph?
$f(x)=2\sqrt{x + 4}$
a. the function is strictly increasing.
b. the function is strictly decreasing.
c. the function is increasing and decreasing.
d. the function is constant.

Explanation:

1. Analyze the function $f(x)=2\sqrt{x+4}$: The square root function $\sqrt{x+4}$ is defined for $x \geq -4$, and as $x$ increases, the value inside the square root increases, making $\sqrt{x+4}$ increase. Multiplying by a positive constant (2) preserves this increasing behavior.
2. Observe the graph: The curve moves upward from left to right across its entire domain, meaning as $x$ increases, $f(x)$ always increases, with no intervals where it decreases or stays constant.
3. Match to options: This behavior fits the definition of a strictly increasing function.

Answer:

A. The function is strictly increasing.