1. The problem asks to find the value of $h$ in the function $g(x) = 3^{x - h} + k$ given that $g(x)$ is a horizontal and vertical translation of $f(x) = 3^x$. 2. The function $g(x) = 3^{x - h} + k$ represents a horizontal shift by $h$ units and a vertical shift by $k$ units of the base function $f(x) = 3^x$. 3. A positive $h$ shifts the graph to the right, and a negative $h$ shifts it to the left. 4. The problem states the red curve (graph of $g(x)$) is shifted to the right compared to the blue curve (graph of $f(x)$), indicating $h$ is positive. 5. Among the options $-2, -1, 1, 2$, the positive values are $1$ and $2$. 6. Since the red curve is shifted to the right, $h$ must be positive, so $h = 1$ or $h = 2$. 7. The problem does not specify the exact amount of shift, but the common choice for a single unit shift is $h = 1$. Final answer: $h = 1$