Question

What transformation can you apply to `y=sqrtx` to obtain the graph `y=5sqrt(x+20)`?

Answer 1

Translation:

First we can perform a translation of `20` units to the left to get from:
`y = sqrt(x) \ \ \ \ \` to `\ \ \ \ \ y_1=sqrt(x+20)`

Scale:

Next we scale along the `y`-axis by a factor of `5` to get from
`y_1 = sqrt(x+20) \ \ \ \` to `\ \ \ \ \ y_2 = 5sqrt(x+20)`

We can see this graphically. All graphs are to the same scale

Graph 1 : `y=sqrt(x)`
graph{sqrt(x) [-25, 25, -5, 25]}

Graph 2 : `y=sqrt(x+20)`
graph{sqrt(x+20) [-25, 25, -5, 25]}

Graph 2 : `y=5sqrt(x+20)`
graph{5sqrt(x+20) [-25, 25, -5, 25]}