Question: Write a function $g$ whose graph represents the indicated transformation of the graph of $f$.
$f(x) = 3x$; translation 5 units up
The translated function is $g(x) = \square$.
1. **State the problem:** We are given a function $f(x) = 3x$ and asked to find a function $g(x)$ that represents the graph of $f$ translated 5 units up.
2. **Recall the translation rule:** Translating a graph vertically by $k$ units up means adding $k$ to the function output. So if $f(x)$ is the original function, the translated function is:
$$g(x) = f(x) + k$$
where $k = 5$ in this case.
3. **Apply the translation:** Substitute $f(x) = 3x$ and $k = 5$:
$$g(x) = 3x + 5$$
4. **Interpretation:** This means every output value of $f(x)$ is increased by 5, shifting the entire graph up by 5 units.
**Final answer:**
$$g(x) = 3x + 5$$