I'll do a couple
1.If f(x) =√3x+3 , what is the equation for f^–1(x)?
Let
\(Let\;\;y=f(x)\\ y=\sqrt3x+3\\ y-3=\sqrt3x\\ \frac{y-3}{\sqrt3}=x\\ x=\frac{\sqrt3(y-3)}{3}\\~\\ f^{-1}(x)=\frac{\sqrt3(x-3)}{3}\\~\\ \)
2.If the parent function is √x, describe the translation of the function √x+7
This is a translation 7 units up
3.Rewrite y = √9x+45 +2 to make it easy to graph using a translation. Describe the graph.
y = √9x+45 +2
y = 3x+47
The parent graph could be y=3x gradient is 3 moved up so the y intercept is 47