1.5 Continuity
This is the fifth lesson in the Limits Unit. The lesson contains Guided Notes, homework, SmartBoard lesson, and all solutions. Don’t forget the added bonus of a math joke embedded into the Smartboard lesson ☺! You may have also opted to purchase the video lesson to the notes.

In this lesson, students will learn all about continuity. This lesson is typically one of the hardest lessons in the Limits Unit, so I tried to break down each topic. I also like to spend a little more time on this topic compared to the other sections in limits. Additionally, continuity is often on the AP Exam. We start the lesson discussing the definition of continuity, and determining which one of the three conditions (if any) fails by looking at a graph. Next, we discuss the three types of discontinuities and how looking at some functions forms holes and vertical asymptotes. Then, we determine how looking at piecewise functions forms breaks. Here, I make sure the students go through each step in the definition of continuity to prove (or disprove) continuity. Finally, I noticed the creators of the AP exams like to have students solve for k in several different ways. Continuity is one of those ways. For the last part of the notes, the students will be solving for k in order to make a function continuous.

I hope you find the notes easy to follow. Please feel free to offer any suggestions on how to make them better as well! Through a community of collaboration, we can find that “sweet spot” for our students and their learning process.

All the best,
Allison