1 Answer

Robert J · Answer 1 · 2023-09-03T03:58:27+0000

We will have the following:

First, we can see that the function in the image will have a mother function:

$y=\sqrt[3]{x}$

Where the function has been moved 2 units left, and 2 units down:

$y=\sqrt[3]{x+2}-2$

Now, we known that the function has been expanded on the vertical, so:

$y=a\sqrt[3]{x+2}-2$

Now, we solve for "a" while we replace for a value of the function, we can see that (6, 4) belongs, so:

$\begin{gathered} 4=a\sqrt[3]{6+2}-2\Rightarrow4=a\sqrt[3]{8}-2 \\ \\ \Rightarrow6=2a\Rightarrow a=3 \end{gathered}$

So, the equation of the function will be:

$g(x)=3\sqrt[3]{x+2}-2$

This can be seeing as follows:

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