Question

This is algebra 2 ( function graphs) I’m usually okay with math but I been I of school recently for surgery and forgot a little bit I just need a refresher

Answer 1

The red function has the form of:

$f(x)=\sqrt[]{-x+1}$

In order to obtain the green function, we need to do a reflection over y-axis, then a translation one unit to the right, a translation 1 unit down, and finally a reflection over the x-axis, so:

$\begin{gathered} g(x)=-(\sqrt[]{-(-x)+1-1}-1) \\ g(x)=-\sqrt[]{x}+1 \end{gathered}$