Question

Someone please help me I was working on this on scratch and ran into a few problems .

Answer 1

From the original function

`f(x)=\sqrt[3]{x}`

a vertical stretch means multiplying f(x) by a number greater than 1. So a vertical stretch by a factor of 4 means multiplying f(x) by 4 so we have

`4\sqrt[3]{x}`

A horizontal shrink means dividing the graph by that factor, bringing it closer to the y-axis, so the x-coordinate should be divided by that factor.

Hence a horizontal shift by a factor of 1/3 means dividing x by 1/3, which is same as multiplying x by 3, so we have

`\begin{gathered} =4\sqrt[3]{x*3} \\ g(x)=4\sqrt[3]{3x} \end{gathered}`

Hence Mike is correct.

Also let us compare their graphs

This is Mike's graph

And this is Lucy's graph

You can see that Mike's graph is more stretched (by a factor of 4) than that of Lucy (by a factor of 3)

Hence Mike is correct