We are given the following function:
![f(x)=\sqrt[3]{x}](https://img.qammunity.org/2023/formulas/mathematics/high-school/bpa3vuuo5dtqkg0vqcw69omticpmu0m3k9.png)
If we want to stretch a graph vertical we must multiply the function by the factor we want to stretch it:

Therefore, if we want to stretch the given function by a factor of 4 we must multiply the given function by 4:
![g(x)=4\sqrt[3]{x}](https://img.qammunity.org/2023/formulas/mathematics/college/ewtk6qlhvlfqbj17fuorb46k5qmmotuyit.png)
To shrink the function horizontally we must do the following change:

Therefore, the new function must be:
![g(x)=4\sqrt[3]{(x)/((1)/(3))}](https://img.qammunity.org/2023/formulas/mathematics/college/eenqwtqkx5ixzs0gb4z3tgs6lclwbgggyh.png)
Simplifying we get:
![g(x)=4\sqrt[3]{3x}](https://img.qammunity.org/2023/formulas/mathematics/college/3j6f5cp9lz6orsk2ldpi92q0b4akw2cior.png)
Now, we graph both functions. We get:
The blue graph represents the original function, and the green graph represent the modified function