Question

How do you transform `f(x)=sqrt (x)` into `g(x)=4*sqrt(3(x-1))+8` ?

Answer 1

Please see the explanation below

Explanation:

To transform from

`f(x)=sqrtx`

to

`g(x)=4sqrt(3(x-1))+8`

The `8` is a vertical shift

graph{(y-sqrtx)(y-sqrtx-8)=0 [-10, 10, -5, 5]}

The `4` is a vertical stretch

graph{(y-sqrtx)(y-4sqrtx)=0 [-16.24, 29.37, -4.55, 18.27]}

The `3` is a horizontal stretch

graph{(y-sqrtx)(y-sqrt(3x))=0 [-16.24, 29.37, -4.55, 18.27]}

The `-1` is a horizontal shift to the right

graph{(y-sqrt(x))(y-sqrt(x-1))=0 [-9.45, 22.58, -1.15, 14.88]}

And alltogether
graph{(y-sqrtx)(y-4sqrt(3(x-1))-8)=0 [-19.08, 32.23, -5.97, 19.7]}