Answer
$f(x) = 3^x$.
Work Step by Step
RECALL:
(1) In the exponential function above, $\dfrac{f(x+1)}{f(x)} = a$
Using the points $(1, 3)$ and $(2, 9)$ and the formula in (1) above,
$\dfrac{9}{3}=a
\\3 = a$
Thus, the tentative equation of the function is $f(x) = C \cdot 3^x$.
To find the value of $C$, use any point on the graph and substitute the x and y values of the point into the tentative equation above. Using the point (1,3) gives:
$f(x) = C \cdot 3^x
\\3 = C \cdot 3^1
\\3 = C \cdot 3
\\\frac{3}{3} = C
\\1 = C$
Thus, the exponential function whose graph is given is $f(x) = 3^x$.
