1. **State the problem:** We need to identify the exponential function from the given options based on the graph. 2. **Recall the general form of an exponential function:** $$y = a \cdot b^x$$ where $a$ is the initial value (value at $x=0$) and $b$ is the base that determines the growth rate. 3. **Analyze the graph:** - The graph passes through the point approximately $(0, 2)$, so $y(0) = a \cdot b^0 = a = 2$. - The graph is increasing, so the base $b$ must be greater than 1. 4. **Check each option at $x=0$:** - F: $y = 2 \cdot 2^0 = 2 \cdot 1 = 2$ - G: $y = 4 \cdot 4^0 = 4 \cdot 1 = 4$ - H: $y = 4 \cdot 2^0 = 4 \cdot 1 = 4$ - J: $y = 2 \cdot 4^0 = 2 \cdot 1 = 2$ Only options F and J have $y=2$ at $x=0$. 5. **Check the growth rate by evaluating at $x=1$:** - F: $y = 2 \cdot 2^1 = 2 \cdot 2 = 4$ - J: $y = 2 \cdot 4^1 = 2 \cdot 4 = 8$ 6. **Compare with the graph:** The graph rises to about 4 at $x=1$, not 8. 7. **Conclusion:** The function is $$y = 2 \cdot 2^x$$ which corresponds to option F.