Determine whether the following statement is true or false: "If \( \lim _{x \rightarrow 3} f(x)=7 \), then \( \lim _{x \rightarrow 3^{-}} f(x)=7 \).

**True.** **Explanation:** For the two-sided limit \(\lim_{x \rightarrow 3} f(x) = 7\) to exist, both the left-hand limit \(\lim_{x \rightarrow 3^-} f(x)\) and the right-hand limit \(\lim_{x \rightarrow 3^+} f(x)\) must exist and be equal to each other. Specifically: 1. **Two-Sided Limit Exists:** \(\lim_{x \rightarrow 3} f(x) = 7\) implies that as \(x\) approaches 3 from both the left and right, the function \(f(x)\) approaches 7. 2. **Left-Hand Limit:** Since the two-sided limit exists and equals 7, it necessarily follows that \(\lim_{x \rightarrow 3^-} f(x) = 7\). 3. **Right-Hand Limit:** Similarly, \(\lim_{x \rightarrow 3^+} f(x) = 7\). Therefore, the statement "If \( \lim _{x \rightarrow 3} f(x)=7 \), then \( \lim _{x \rightarrow 3^{-}} f(x)=7 \)" is **true**.