Question

What is the end behavior of the function f(x)=-2^2\root(3)(x)

Answer 1

Using limits, it is found that the end behavior of the function is:

• It goes to 0 as x goes to negative infinity.

• It goes to positive infinity as x goes to positive infinity.

How do we find the end behavior of a function?

We find it by finding the limit of the function as x goes to infinity.

In this problem, the function is:

$f(x) = -2^{2\sqrt[3]{x}}$

Hence, the limits are:

$\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -2^{2\sqrt[3]{x}} = -2^{-\infty} = 0$

$\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -2^{2\sqrt[3]{x}} = -2^{\infty} = \infty$

The end behavior of the function is:

• It goes to 0 as x goes to negative infinity.

• It goes to positive infinity as x goes to positive infinity.

More can be learned about limits at https://brainly.com/question/22026723