select the correct answer.\nwhat is the end - behavior of this radical function?\n$f(x)=-2\\sqrt3{x +…

select the correct answer.\nwhat is the end - behavior of this radical function?\n$f(x)=-2\\sqrt3{x + 7}$\na. as x approaches positive infinity, f(x) approaches negative infinity.\nb. as x approaches negative infinity, f(x) approaches 0.\nc. as x approaches positive infinity, f(x) approaches positive infinity.\nd. as x approaches negative infinity, f(x) approaches negative infinity.

select the correct answer.\nwhat is the end - behavior of this radical function?\n$f(x)=-2\\sqrt3{x + 7}$\na. as x approaches positive infinity, f(x) approaches negative infinity.\nb. as x approaches negative infinity, f(x) approaches 0.\nc. as x approaches positive infinity, f(x) approaches positive infinity.\nd. as x approaches negative infinity, f(x) approaches negative infinity.

Answer

Answer:

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

Explanation:

Step1: Analyze the cube - root function

The function is $f(x)=- 2\sqrt[3]{x}+7$.

Step2: Consider the behavior of $\sqrt[3]{x}$ as $x\to+\infty$

As $x\to+\infty$, $\sqrt[3]{x}\to+\infty$.

Step3: Determine the behavior of $f(x)$ as $x\to+\infty$

Since $f(x)=-2\sqrt[3]{x}+7$ and $\sqrt[3]{x}\to+\infty$ as $x\to+\infty$, then $-2\sqrt[3]{x}\to-\infty$ and $f(x)=-2\sqrt[3]{x}+7\to-\infty$. As $x\to-\infty$, $\sqrt[3]{x}\to-\infty$, and $-2\sqrt[3]{x}\to+\infty$, $f(x)=-2\sqrt[3]{x}+7\to+\infty$. So the end - behavior as $x\to+\infty$ is that $f(x)$ approaches negative infinity.