Question 130631
Since the graph passes through the point (2,9), this means that when x=2, then y=9. 


{{{y=b^x}}} Start with the given equation



{{{9=b^2}}} Plug in x=2 and y=9. Notice how the only unknown left is b



{{{sqrt(9)=sqrt(b^2)}}} Take the square root of both sides to isolate b



{{{sqrt(9)=b}}} Take the square root of {{{b^2}}} to get b



{{{b=3}}} Take the square root of 9 to get 3 



So our equation becomes 



{{{y=3^x}}}



Now to evaluate f(4), simply plug in x=4


{{{y=3^4}}} Plug in x=4



{{{y=81}}} Evaluate 3 to the fourth power to get 81



Since "y" is equivalent to f(x), this means that {{{f(4)=81}}}