Continuity and the Intermediate Value Theorem

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

Define continuity in terms of limits. (§3.2)
Determine where a function is discontinuous on a graph. (§3.2)
Use continuity of Parent Functions to determine limits. (§3.2)
Define left and right continuity in terms of limits. (§3.4)
Determine where a function is continuous using a graph. (§3.3, §3.4)
Determine limits using continuity laws. (§3.5, §3.6)
Determine when continuity laws cannot be applied. (§3.5, §3.6)
Use continuity of Parent Functions and Composition Laws to break limits into smaller parts to solve. (§3.5, §3.6)
Use the definition of continuity to solve for unknowns in a function. (§3.7)
Make a piecewise function continuous. (§3.7)
Prove that certain points exist using the Intermediate Value Theorem. (§3.8)
Determine when Intermediate Value Theorem can (and can’t) be used. (§3.1, §3.8)