Describing Transformations of Radical Functions

We want to describe the transformations of the parent function $f(x)=\sqrt{x}$ represented by $g(x)=\sqrt{x+1}+8.$ 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. $$\begin{array}{c}g(x)=\sqrt{x+1}+8\end{array}$$ We can describe the transformations as a horizontal translation left $1$ unit and a vertical translation up $8$ units. Let's consider the graph of the radical function $f(x)=\sqrt{x}.$

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.