1. Let's clarify the problem: We want to determine if a function can reach a certain limit value. 2. The limit of a function $f(x)$ as $x$ approaches a value $a$ is the value that $f(x)$ approaches as $x$ gets arbitrarily close to $a$. 3. Important rule: A function can approach a limit without ever actually reaching it. 4. However, it is also possible for the function to reach the limit value at $x=a$ if $f(a)$ is defined and equals the limit. 5. For example, if $\lim_{x \to a} f(x) = L$ and $f(a) = L$, then the function reaches the limit. 6. If $f(a)$ is not defined or $f(a) \neq L$, the function does not reach the limit but still approaches it. 7. Therefore, whether the function reaches the limit depends on the function's definition at that point.