We will have the following:
First, we can see that the function in the image will have a mother function:
[tex]y=\sqrt[3]{x}[/tex]
Where the function has been moved 2 units left, and 2 units down:
[tex]y=\sqrt[3]{x+2}-2[/tex]
Now, we known that the function has been expanded on the vertical, so:
[tex]y=a\sqrt[3]{x+2}-2[/tex]
Now, we solve for "a" while we replace for a value of the function, we can see that (6, 4) belongs, so:
[tex]\begin{gathered} 4=a\sqrt[3]{6+2}-2\Rightarrow4=a\sqrt[3]{8}-2 \\ \\ \Rightarrow6=2a\Rightarrow a=3 \end{gathered}[/tex]
So, the equation of the function will be:
[tex]g(x)=3\sqrt[3]{x+2}-2[/tex]
This can be seeing as follows:
