Ok, so
Here we have the following piecewise function.
First, notice that the yellow function is a function which comes from some changes to the function:
If we modify the previous function to get the yellow one, we obtain that the yellow function will be:
Notice that this function will exist if
Now, let's see the blue function. As you can see, it has the form of an absolute value function.
Now, our blue function is a function which comes from some changes to the function:
If we modify the previous function to get the blue one, we obtain that the blue function will be:
Notice that the function exists if:
If we modify the previous function to get the green one, we obtain that the green function will be:
As this is a piecewise function, we could write the solution as:
[tex]f(x)=\begin{cases}-3\sqrt[]{-x-4}-1\text{ if }x\leq-4 \\ y=\lvert\frac{3}{2}x+3\lvert-1\text{ if }4