Understanding continuity in a function might seem tricky at first, but it’s not too hard once you break it down!

A function is considered continuous at a certain point if it meets three important rules:

1. The Function Has a Value: First, check if the function actually has a value at the spot you’re looking at. For example, if you’re looking at $f(c)$, make sure that $f(c)$ is a real number.

2. Limit Exists: Next, see if the limit of the function is there as it nears that point. This part involves limits! You’ll need to find $\lim_{x \to c} f(x)$. If the left side limit ($\lim_{x \to c^-} f(x)$) and the right side limit ($\lim_{x \to c^+} f(x)$) both exist and are the same, then the overall limit is there too.

3. Limit Equals Function Value: Lastly, you should check if the limit you found matches the function’s value at that spot. So you want to see if $\lim_{x \to c} f(x) = f(c)$.

If you can check off all three of these items, then you can happily say that the function is continuous at that point!

To put it simply, think of continuity like a smooth line with no breaks or jumps in it. If you can draw the graph of the function at that point without picking up your pencil, then it’s continuous there.

This easy way of thinking can really help if you’re learning about limits and continuity in pre-calculus for the first time.