One-sided limits are really helpful for understanding how functions behave! Let’s break it down:

1. What They Are: A one-sided limit looks at what happens to a function as it gets close to a certain point from one side—either the left or the right. For example, we write the left side limit at $x = a$ like this: $\lim_{x \to a^-} f(x)$. The right side limit is written as $\lim_{x \to a^+} f(x)$.

2. Checking for Continuity: A function $f(x)$ is considered continuous at a point $x = a$ if:

   • The limit exists: $\lim_{x \to a} f(x)$.
   • The function value is defined: $f(a)$ exists.
   • The limit and the function value are the same: $\lim_{x \to a} f(x) = f(a)$.

3. Spotting Problems: If the left and right limits aren’t the same, it means there might be a jump or other issues with the function. This is useful for drawing graphs and seeing how the function behaves near that point.

So, you can think of one-sided limits like little detectives that help us figure out what's going on with functions at tricky spots!