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.
  • Bisection method.