1. **State the problem:** We are given two functions $f(x) = \sin x$ and $g(x) = 3$, and we need to find the range of the combined function $$y = f(x) + g(x) = \sin x + 3.$$ 2. **Recall the range of $\sin x$:** The sine function oscillates between $-1$ and $1$, so its range is $$-1 \leq \sin x \leq 1.$$ 3. **Add the constant function $g(x) = 3$ to $f(x)$:** Adding 3 shifts the entire sine wave up by 3 units. So the new function's values will be $$y = \sin x + 3.$$ 4. **Calculate the new range:** Since $\sin x$ ranges from $-1$ to $1$, adding 3 gives $$-1 + 3 \leq y \leq 1 + 3,$$ which simplifies to $$2 \leq y \leq 4.$$ 5. **Interpretation:** The combined function $y$ takes all real values between 2 and 4 inclusive. **Final answer:** The range of $y = \sin x + 3$ is $$\{ y \in \mathbb{R} : 2 \leq y \leq 4 \}.$$ This corresponds to option d).