Question

Given f(x)=2^x and g(x)=f(x-3)+4, write the new function rule (equation) for function g and describe (using words*) the two transformations that occur between function f and function g.

Answer 1

Answer:

• The first thing we do is find out what f(x-3) is
• $f(x)=2^x\\f(x-3)=2^{x-3}$ this is can be simplified using the rules of exponents
• $f(x-3)=2^{x-3}\\f(x-3)=2^x\div2^3\\f(x-3)=\frac{2^{x}}{8}$
• Then we put that into g(x)
• $g(x)=f(x-3)+4\\g(x)=\frac{2^{x}}{8}+4$
• The first transformation is at f(x), where it is divided by 8, and then inserted into g(x) which increases the new transformed f(x) by 4