Question

Given `f(x) = root3x`, what is the translation of `g(x) = 5root3(x+2) - 2`?

Answer 1

`g(x)=5f(x-2)-2`

Explanation:

First we know that the translation form of any funciton looks like

`x^2 rArr A[B(x-C)]^2+D`
`sin(x)rArr Asin[B(x-C)]+D`
`ln(x)rArr Aln[B(x-C)]+D`
`sqrt(x)rArr Asqrt[B(x-C)]+D`

With
A~ Vertical stretch, streches the y values by A
B~ Horizontal stretch, streches the x values by `1/B`
C~ Horizontal translation, moves x values over by C
D~ Vertical translation, moves y values up by C

So 5 is the vertical stretch
So -2 is the horizontal translation
So -2 is the vertical translation

So you know the function has been moved 2 to the left and 2 down.

`g(x)=5f(x-2)-2`