Question

select the correct answer.
what is the end behavior of this radical function?
$f(x) = -2\sqrt3{x + 7}$
a. as $x$ approaches positive infinity, $f(x)$ approaches negative infinity.
b. as $x$ approaches negative infinity, $f(x)$ approaches 0.
c. as $x$ approaches positive infinity, $f(x)$ approaches positive infinity.
d. as $x$ approaches negative infinity, $f(x)$ approaches negative infinity.

Explanation:

Step1: Analyze $x\to+\infty$ behavior

As $x\to+\infty$, $x+7\to+\infty$. Then $\sqrt[3]{x+7}\to+\infty$. Multiply by -2: $-2\sqrt[3]{x+7}\to-\infty$.

Step2: Analyze $x\to-\infty$ behavior

As $x\to-\infty$, $x+7\to-\infty$. Then $\sqrt[3]{x+7}\to-\infty$. Multiply by -2: $-2\sqrt[3]{x+7}\to+\infty$.

Answer:

A. As x approaches positive infinity, f(x) approaches negative infinity.