Describing Transformations of Radical Functions

We want to describe the transformations of the parent function $f(x)=\sqrt[3]{x}$ represented by $g(x)=\sqrt[3]{x+4}-5.$ To do so, let's look at the possible transformations. Then, we can more clearly identify the ones being applied.

Now, using the table, let's highlight the transformations. $$\begin{array}{c}g(x)=\sqrt[3]{x+4}-5\end{array}$$ We can describe the transformations as a horizontal translation left $4$ unit and a vertical translation down $5$ units. Let's consider the graph of the rational function $f(x)=\sqrt[3]{x}.$

Next, we will apply the transformations to the graph of $f(x)$ to obtain the graph of $g(x).$

Therefore, we have the graph of each function.