1. The problem asks for a function with domain all real numbers and range all real numbers less than or equal to 3. 2. This means the function can take any real input $x \in \mathbb{R}$, but the output $y$ must satisfy $y \leq 3$. 3. A common example is a function that has a maximum value of 3 and decreases or stays below 3 for all $x$. 4. One such function is $y = 3 - x^2$. 5. The domain of $y = 3 - x^2$ is all real numbers because $x^2$ is defined for all $x \in \mathbb{R}$. 6. The range is all $y$ such that $y \leq 3$ because $x^2 \geq 0$ for all $x$, so $3 - x^2 \leq 3$. 7. The graph is a downward opening parabola with vertex at $(0,3)$, which is the maximum point. 8. This satisfies the problem conditions perfectly. Final answer: The function $y = 3 - x^2$ has domain $\mathbb{R}$ and range $(-\infty, 3]$.