False; consider as a counterexample the function f : ℝ→ℝ defined by
[tex]f(x)=\begin{cases}-3&\text{for }x\neq2\\0&\text{for }x=2\end{cases}[/tex]
Clearly f approaches -3 as x gets closer to -2, but neither limit from either side is equal to the function's value at x = 2 (that is, -3 ≠ 0), so f is not continuous.
