Continuity and the IVT

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After completing this section, you should be able to do the following.

State the three components of the limit definition of continuity.
Identify the locations of discontinuities of a function.
Identify the intervals on which a function is continuous.
Identify which common functions are continuous on their domains.
Make a piece-wise function continuous.
State the Intermediate Value Theorem (hypotheses and conclusion).
Determine if the Intermediate Value Theorem applies to a given situation.
Sketch pictures indicating why the Intermediate Value Theorem is true and why all hypotheses are necessary.
Explain why certain points exist using the Intermediate Value Theorem.

Skills you may want to brush up on first
To be ready to achieve these objectives, you may need to review the following trigonometry and algebra topics:

Common types of functions: power functions, polynomial functions, and rational functions
Composition of Functions