Continuity and the Intermediate Value Theorem

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

Identify where a function is, and is not, continuous.
Understand the connection between continuity of a function and the value of a limit.
Make a piecewise function continuous.
State the Intermediate Value Theorem including hypotheses.
Determine if the Intermediate Value Theorem applies.
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.