1. The problem asks about the continuity of a function $f$ at a point $x=a$ where the graph has a break or jump. 2. The definition of continuity at $x=a$ is that the limit of $f(x)$ as $x$ approaches $a$ exists and equals $f(a)$. 3. A break or jump in the graph at $x=a$ means the left-hand limit and right-hand limit at $a$ are not equal, or the function value $f(a)$ does not match these limits. 4. Therefore, if there is a break or jump at $x=a$, the function $f$ is discontinuous at $x=a$. 5. This statement is always true, so the correct answer is (d) true.