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

1 Answer
Apr 1, 2018

#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#