The graph of a function is like a picture that shows how the function behaves. It can help us see if the function is continuous or has breaks. Here are some important points to understand:

1. Continuity: A function is continuous at a point called $c$ if these three things are true:

   • We can find the value of the function at $c$, which we call $f(c)$.
   • As we get closer to $c$, the values of the function approach a certain number, which we write as $\lim_{x \to c} f(x)$, and this limit exists.
   • The value when we get close to $c$ is the same as the value at $c$. In other words, $\lim_{x \to c} f(x) = f(c)$.

2. Discontinuity: A function can have breaks at certain points called discontinuities. Here’s how they show up:

   • There might be an "open hole" (removable discontinuity). This means that even though limits exist, we can't find a value for $f(c)$.
   • There might be a "jump" (jump discontinuity). This happens when the values from the left and right sides of $c$ are not equal.
   • There could be an "infinite" discontinuity. Here, the function goes up to infinity as we get close to a point.

By looking at the graph, we can easily see if the function is continuous or has breaks. This is a helpful way to study how a function behaves!