Answer
$2\cdot 3^{x}$.
Work Step by Step
1. The given graph resembles that of an exponential function with a form $y=ka^{x}$ where $k, a$ are parameters.
2. Use the point $(0,2)$, we have $2=k$, thus $y=2a^{x}$.
3. Use the point $(1,6)$, we have $6=2a^{1}$, thus $a=3$.
4. The answer is $f(x)=2\cdot 3^{x}$.
