Graph of f(x-3) is compressed by a factor of [tex]\frac{1}{8}[/tex] horizontally of f(x).
Step-by-step explanation:
We have, the graph of f(x)= [tex]2^{x}[/tex] , on replacing f(x) by f(x-3) we get:
[tex]f(x-3)[/tex]= [tex]2^{x-3} = \frac{2^{x}}{2^{3}} = \frac{1}{8} 2^{x} = \frac{1}{8} f(x)[/tex].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 [tex]\frac{1}{8}[/tex] horizontally . Domain and range of both functions are same i.e. F(x) & f(x-3) domain & range are same , just difference in graph : [tex]f(x-3) = \frac{1}{8} f(x)[/tex].
