For a function $f$ to be continuous at $x = a$, the following condition must be satisfied:

$\lim_{{x \to a}} f(x) = f(a)$

In detail, this means:

1. The limit of $f(x)$ as $x$ approaches $a$ must exist.
2. $f(a)$ must be defined.
3. The limit of $f(x)$ as $x$ approaches $a$ must be equal to $f(a)$.

If all three of these conditions are met, the function $f$ is continuous at $x = a$.

Would you like further details or explanations on continuity concepts?

Here are some related questions that might enhance your understanding:

1. What does it mean for a function to be continuous on an interval?
2. How does continuity relate to differentiability?
3. What is the difference between continuity at a point and uniform continuity?
4. How can we check continuity for piecewise functions?
5. What are the implications of discontinuities in real-world applications?

Tip: Continuity can often be visually analyzed by checking if you can draw a function without lifting your pencil; if so, it's continuous on that interval.