The question is a straight forward 7th grade question with no exposure to logs. Given some parent graph shown in red, (which is easy for me to see is $y=2^x$, what is the transformed graph shown in blue, given that the transformed graph looks like (see included) and has the following 2 ordered pairs $(2,25), (-1,0.2)$. It's easy for me to see that the new function is $y=5^x$. However, this represents a change in the "b" value of $y=ab^x$ and I know that for this transformation it should be a horizontal compression or stretch NOT a change in the "b" value, but rather a change in the coefficient in front of the $x$ term.
How do I determine what the transformation is? These values are easy to see, but I want to understand the process so that if I had more complex problems I could see what the process is.
My thought is that given the parent graph of $y=ab^x$, the transformation would represent a change in the coefficient in front of the $x$ value. Specifically, there should be in the transformed graph a term $y=ab^\left(cx\right)$, where I need to determine the value of c.