Master method recurrence question This is specifically a question pertaining to solving reccurences via the Master Theorem/Method, particularly for a specified $f(n)$ (as denoted below).

For a recurrence of $$T(n) = a T(\frac{n}{b}) + f(n)$$ 

where f(n) is $\Theta{(n)}$, would we be comparing $n^{\log_b(a)}$ with $n^{1}$ - meaning we would be comparing $log_b(a)$ with 1? Since the rate of growth is linear?

what about where f(n) is $\Theta{(1)}$ (aka some constant?), would we be comparing $n^{\log_b(a)}$ with $n^{0}$? '0' since there is no rate of growth for a constant?
I think the question is asking how to translate $f(n)$ into Big-Theta notation to be used for the Master Theorem. You have the right idea about switching between notations. 

Another way to write the Master Theorem is as follows: 

$T(n) = aT(n/b) + \Theta(n^d)$

So, yes, if you have a linearly growing function, then $f(n)$ may be substituted with $\Theta(n)$.

Then you may proceed with your comparisons.