Question

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

a. y = 0
b. y = 3
c. y = 4
d. y = 5

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)`