Ch 5: Function Continuity

About This Chapter

Enhance your understanding of continuous functions and theorems which work with them with the engaging videos in this chapter. Use the quizzes and chapter test to get a feel for how well you have retained key information and formulae.

Function Continuity - Chapter Summary and Learning Objectives

Our expert instructors will help you boost your knowledge of continuous function theorems such as the intermediate value and Bolzano's theorems. The brief quizzes after each lesson and the test at the end of the chapter are designed to give you an idea of where you strengths and weaknesses in this topic lie. The information covered in this chapter include:

  • Definitions and examples of continuities and discontinuities in functions and graphs
  • Examples and uses of the Intermediate Value Theorem
  • Other continuous function theorems, including Extreme Value and Bolzano's

Video Objective
Continuity in a Function Here our instructors set out the rules for what qualifies as a continuous function (it is a function which does not have any breaks in its line, by the way).
Discontinuities in Functions and Graphs This lesson describes several different types of discontinuities.
Regions of Continuity in a Function In this video you'll learn about functions which have continuous sections between points of discontinuity.
Intermediate Value Theorem: Definition Though it may go without saying, this lesson discusses the theorem which says that a line that is continuous between two points meets every value between those points at least once.
Intermediate Value Theorem: Examples and Applications Our instructors walk you through a few examples of the intermediate value theorem here.
Extreme Value Theorem & Bolzano's Theorem Learn about a few other theorems which work with continuous functions in this brief video.
Continuous Functions Theorems Still more theorems working with continuous functions are described here.

6 Lessons in Chapter 5: Function Continuity
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.

Intermediate Value Theorem: Definition

4. 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

5. 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.

Extreme Value Theorem & Bolzano's Theorem

6. 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.

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

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