2.1 Continuity

In this lesson, you will learn about continuity.

Lesson Objectives

Upon completion of the lesson 2.1, you will be able to:

• • Visually recognize continuities and discontinuities from graphs.

  • Apply the definition of continuity at a point to determine whether a function is continuous at a point.

  • Find points of discontinuity.

  • Classify discontinuities.

  • Apply continuity rules (sum, diff., constant multiple, product, quotient, power, root) & theorems (continuity of polynomial, rational, composite, trig. functions) to determine whether a function is continuous at a point or on an interval.

  • Apply the Intermediate Value Theorem.

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

• 1. YouTube video: Continuity of a Function

• 1. YouTube video: Continuous Functions

• 1. YouTube videos: Continuity

  2. Part 1:

• 1. Part 2:

• 1. YouTube video: Intermediate Value Theorem

• 1. Continuity [University of Houston] (watch pages 1 – 10 only)

  2. ouTube video: Intermediate Value Theorem Examples

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

• 1. Limits & Continuity: Lesson 15- Continuity [Internet Archive] The module includes information on continuity at a point, continuity on a closed interval, continuity on an open interval, intermediate value theorem, and homework.

1. Continuity [Paul's Online Math Notes]

   1. Lesson 7: Continuity [Prairie State College Read page 24: Classifying discontinuities.

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

• 1. Continuity Help Materials (Solutions provided)br> Continuity at a Point [University of Houston]

  2. Continuity on an Interval [University of Houston]

  3. One-sided Continuity [University of Houston]

  4. Intermediate Value Theorem [University of Houston] Do #1 and #3 only.

  5. Continuity [Paul's Online Math Notes] (solutions provided)

  6. Classifying Discontinuities [saskschools.ca] (solutions provided)

Additional Resources

Below are additional resources that help reinforce the content for this module.

1. Continuity

   1. Continuity [UMass Lowell] (definition of continuity, continuity and algebraic combinations, continuity of a composition, the intermediate value theorem)

   2. >Continuity [CliffsNotes]