Function transformation involves changing the form of a function
The function g(x) is
The function is given as:
g(x) is an exponential function that passes through points (-2,2) and (-1,4).
An exponential function is represented as:
At point (-2,2), we have:
At point (-1,4), we have:
Divide both equations
Simplify
Apply law of indices
Rewrite as:
Substitute 2 for b in
This gives
Multiply both sides by 4
Substitute 8 for (a) and 2 for (b) in
Express as a function
Hence, the function g(x) is
Read more about exponential functions at: