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 
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