1. The problem states that the graph represents the function $y = a^x$ and passes through the point $(0,1)$. 2. Recall that for any exponential function $y = a^x$, when $x=0$, $y = a^0 = 1$ regardless of the value of $a$ (as long as $a \neq 0$). 3. To find $a$, we need another point on the graph. From the description, the graph rises steeply and the y-axis is labeled up to 6 at $x=2$. 4. Assume the graph passes through the point $(2, y_2)$ where $y_2$ is approximately 4 (since the curve rises steeply and the y-axis goes up to 6). 5. Using the point $(2,4)$, substitute into the equation: $$4 = a^2$$ 6. Solve for $a$: $$a = \sqrt{4} = 2$$ 7. Therefore, the value of $a$ is 2. Final answer: $a = 2$