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

• 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/2^3\\f(x-3)=(2^(x))/(8)`
• Then we put that into g(x)
• 
  `g(x)=f(x-3)+4\\g(x)=(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