Two points that the exponential function passes through are (0,1) and (1,2).
The general form of an exponential function is $f(x) = ab^x$.
Using the point (0,1), we have $1 = ab^0 = a$. Thus, $a=1$.
Using the point (1,2), we have $2 = (1)b^1 = b$. Thus $b=2$.
The exponential function is $f(x) = 2^x$.
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