Question: Select the correct answer.
Consider the function graphed below.
If $f$ is translated 4 units down to create $g$, which function represents $g$?
g(x) = f(x) + 4
g(x) = f(x - 4)
g(x) = f(x) - 4
g(x) = f(x) + 4
graph: exponential curve labeled $f$ in the center-left, with horizontal asymptote near $y = 2$ and increasing steeply to the upper-right; position_hint=center
1. **State the problem:** We have a function $f$ and want to find the function $g$ that results from translating $f$ down by 4 units.
2. **Recall the translation rule:** Translating a function vertically down by $k$ units means subtracting $k$ from the function's output.
3. **Apply the rule:** Since the translation is 4 units down, we subtract 4 from $f(x)$:
$$g(x) = f(x) - 4$$
4. **Check other options:**
- $g(x) = f(x) + 4$ translates the graph up by 4 units.
- $g(x) = f(x - 4)$ translates the graph 4 units to the right (horizontal shift).
5. **Final answer:**
$$\boxed{g(x) = f(x) - 4}$$