Here are the main points that will be addressed in the videos. Please read these and think about them as you watch.

• Functions that “look” continuous on a graph may not actually be continuous.
• A function $f$ is continuous at $a$ if $\lim \limits _{x \to a} f(x) = f(a)$. Implicit in this definition are three conditions for continuity of $f$ at $a$:

  (a)

  the function $f$ is defined at $a$,

  (b)

  the limit of $f(x)$ as $x \to a$ exists, and

  (c)

  the limit and function values are equal.

• When a function $f$ is NOT continuous at $a$, then at least one of the three conditions above are not satisfied.