1. The problem asks to identify the domain of the function $f$ based on the given graph description. 2. The domain of a function is the set of all possible input values ($x$-values) for which the function is defined. 3. The graph is a parabola opening upwards with vertex at approximately $(0, -12.25)$. 4. Since it is a parabola opening upwards, it extends infinitely to the left and right along the $x$-axis. 5. Therefore, the domain includes all real numbers because there are no restrictions on $x$ for a parabola. 6. The options given are: - $-4 \leq x \leq 5$ - All real numbers - $y \geq -12.25$ - All real numbers less than $-4$ or greater than $5$ 7. The correct domain is "All real numbers" because the parabola extends infinitely in both directions along the $x$-axis. Final answer: The domain of $f$ is all real numbers.