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:
[tex]y=\sqrt[]{x}[/tex]
If we modify the previous function to get the yellow one, we obtain that the yellow function will be:
[tex]y=-3\sqrt[]{-x-4}-1[/tex]
Notice that this function will exist if
[tex]x\leq-4[/tex]
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:
[tex]y=\lvert x\rvert[/tex]
If we modify the previous function to get the blue one, we obtain that the blue function will be:
[tex]y=\lvert\frac{3}{2}x+3\lvert-1[/tex]
Notice that the function exists if:
[tex]-4Now and finally, the green function has the form of a translated cubic root.
Our green function is a function which comes from some changes to the function:
[tex]y=\sqrt[3]{x}[/tex]
If we modify the previous function to get the green one, we obtain that the green function will be:
[tex]y=2\sqrt[3]{x-6}+4[/tex]
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
