Question

What is the effect on the graph of the function f(x) = 2^x when f(x) is replaced with f(x − 3)?

Answer 1

Graph of f(x-3) is compressed by a factor of
`(1)/(8)` horizontally of f(x).

Explanation:

We have, the graph of f(x)=
`2^(x)` , on replacing f(x) by f(x-3) we get:

`f(x-3)`=
`2^(x-3) = (2^(x))/(2^(3)) = (1)/(8) 2^(x) = (1)/(8) f(x)`.Below shown are the images for graph of f(x) and f(x-3). Both are functions are exponential , and so having exponential graph but f(x-3) is compressed by a factor of
`(1)/(8)` horizontally . Domain and range of both functions are same i.e. F(x) & f(x-3) domain & range are same , just difference in graph :
`f(x-3) = (1)/(8) f(x)`.