The function
is a cube root function
The function end behavior is:
![\quad \mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty](https://tex.z-dn.net/?f=%5Cquad%20%5Cmathrm%7Bas%7D%5C%3Ax%5Cto%20%5C%3A%2B%5Cinfty%20%5C%3A%2C%5C%3Af%5Cleft%28x%5Cright%29%5Cto%20%5C%3A%2B%5Cinfty%20%5C%3A%2C%5C%3A%5C%3A%5Cmathrm%7Band%5C%3Aas%7D%5C%3Ax%5Cto%20%5C%3A-%5Cinfty%20%5C%3A%2C%5C%3Af%5Cleft%28x%5Cright%29%5Cto%20%5C%3A%2B%5Cinfty)
<h3>How to determine the end behavior?</h3>
The equation of the function is given as:
![f(x) = 4\sqrt[3]{x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%204%5Csqrt%5B3%5D%7Bx%7D)
To determine the end behavior, we plot the graph of the function f(x).
From the attached graph of the function, we can see that:
As x approaches infinity, the function f(x) approaches infinity, and vice versa
Hence, the function end behavior is:
![\quad \mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty](https://tex.z-dn.net/?f=%5Cquad%20%5Cmathrm%7Bas%7D%5C%3Ax%5Cto%20%5C%3A%2B%5Cinfty%20%5C%3A%2C%5C%3Af%5Cleft%28x%5Cright%29%5Cto%20%5C%3A%2B%5Cinfty%20%5C%3A%2C%5C%3A%5C%3A%5Cmathrm%7Band%5C%3Aas%7D%5C%3Ax%5Cto%20%5C%3A-%5Cinfty%20%5C%3A%2C%5C%3Af%5Cleft%28x%5Cright%29%5Cto%20%5C%3A%2B%5Cinfty)
Read more about function end behavior at:
brainly.com/question/23968442