Question

Which function represents a horizontal shift of ƒ(x) = 5(2)^3x by 4 units to the right?

Answer 1

General Idea:

Say if f(x) is the parent function, then f(x-c) represents transformation described as horizontal translation or shift of f(x) by ' c ' units to the right.

Applying the concept:

Here we are given a function $f(x)=5(2)^{3x}$, after the transformation of horizontal shift of 4 units to the right, the function will be given as below:

$f(x)=5(2)^{3(x-4)}=5(2^{3})^{x-4}=5(8)^{x-4} \\ or\\ f(x)=5(2)^{3x-12}$