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  $\frac{1}{8}$ horizontally of f(x).

Step-by-step explanation:

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

$f(x-3)$= $2^{x-3} = \frac{2^{x}}{2^{3}} = \frac{1}{8} 2^{x} = \frac{1}{8} f(x)$.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  $\frac{1}{8}$ horizontally . Domain and range of both functions are same i.e. F(x) & f(x-3) domain & range are same , just difference in graph : $f(x-3) = \frac{1}{8} f(x)$.