1. The problem asks about the behavior of the function $f$ at a point $x=a$ where the graph has a break or jump. 2. The statement is: "If the graph of the function $f$ has a break or jump at $x=a$, then the limit $\lim_{x \to a} f(x)$ does not exist." 3. Important rule: The limit $\lim_{x \to a} f(x)$ exists only if the left-hand limit $\lim_{x \to a^-} f(x)$ and the right-hand limit $\lim_{x \to a^+} f(x)$ both exist and are equal. 4. A break or jump in the graph at $x=a$ means the left-hand and right-hand limits are not equal, so the limit does not exist. 5. However, sometimes a function can have a removable discontinuity (a hole) where the limit exists but the function is not defined or has a different value at $x=a$. 6. Therefore, the statement is "always true" for jump discontinuities but not for all types of breaks. 7. The best answer is (d) sometimes true because the limit may or may not exist depending on the type of discontinuity. Final answer: (d) sometimes true.