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Ch 13: Saxon Calculus: Continuity as a Property of Functions

About This Chapter

The Continuity as a Property of Functions chapter of this Saxon Calculus Companion Course aligns with the same chapter in the Saxon Calculus textbook. These simple and fun video lessons are about five minutes long and help you learn the essential lessons about continuity and discontinuity as properties of functions.

How It Works:

  • Find the lesson within this chapter that corresponds to what you're studying in the Continuity as a Property of Functions chapter of your textbook.
  • Watch fun videos that cover the calculus concepts you need to learn or review.
  • Complete the quiz after watching each video lesson to test your understanding.
  • If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.

Chapter Topics

You'll learn all of the calculus topics covered in the textbook chapter, including:

  • Understanding continuity and discontinuity in functions and graphs
  • Identifying regions of continuity
  • Balzano's theorem and the extreme value theorem
  • How to use the critical number theorem
  • Polar and interval continuity
  • Definition, applications and examples of the intermediate value theorem

Saxon is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.

9 Lessons in Chapter 13: Saxon Calculus: Continuity as a Property of Functions
Test your knowledge with a 30-question chapter practice test
Continuity in a Function

1. Continuity in a Function

Travel to space and explore the difference between continuous and discontinuous functions in this lesson. Learn how determining continuity is as easy as tracing a line.

Discontinuities in Functions and Graphs

2. Discontinuities in Functions and Graphs

In this lesson, we talk about the types of discontinuities that you commonly see in functions. In particular, learn how to identify point, jump and asymptotic discontinuities.

Regions of Continuity in a Function

3. Regions of Continuity in a Function

Can Earth ever compete with extraterrestrial UFOs? In this lesson, you'll learn that not all functions are continuous, but most have regions where they are continuous. Discover how to define regions of continuity for functions that have discontinuities.

Extreme Value Theorem & Bolzano's Theorem

4. Extreme Value Theorem & Bolzano's Theorem

The extreme value theorem and Bolzano's theorem are two very useful theorems that you can use to help you find solutions as well as maximums and minimums of a function. Learn how to use them in this lesson.

Using the Critical Number Theorem

5. Using the Critical Number Theorem

In this lesson, we will review the statement of the critical number theorem and give several typical examples of its application in locating maximum and minimum values of a function.

Understanding Point Continuity

6. Understanding Point Continuity

Continuity means unbroken or uninterrupted. Some functions are continuous across all values of x, and others aren't. In this lesson, we will discuss point continuity in terms of graphs.

Understanding Interval Continuity

7. Understanding Interval Continuity

Continuity means contiguous or continuing. Graphs of functions are either continuous between two x-values boundaries or not. In this lesson, we will investigate how to determine if a function is continuous in an interval.

Intermediate Value Theorem: Definition

8. Intermediate Value Theorem: Definition

A UFO and a jet take off and ascend to 30,000 feet along discontinuous and continuous paths, respectively. In this lesson, learn about the intermediate value theorem and why the jet has to cross 15,000 feet.

Intermediate Value Theorem: Examples and Applications

9. Intermediate Value Theorem: Examples and Applications

Many problems in math don't require an exact solution. Some problems exist simply to find out if any solution exists. In this lesson, we'll learn how to use the intermediate value theorem to answer an age-old question.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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