Lesson Plan: Continuity of Functions Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to check the continuity of a function over its domain and determine the interval on which it is continuous.


Students will be able to

  • find the interval over which a function is continuous, where the function is given
    • algebraically,
    • graphically,
  • find the value(s) that can be assigned to an unknown in order to make a given function continuous (or discontinuous) over a specified interval,
  • understand the types of functions that are always continuous over their entire domain,
  • understand that piecewise functions may have discontinuities at the endpoints of the subfunctions and must be checked,
  • understand that rational functions have discontinuities at the zeros of their denominator,
  • understand that properties of sums, differences, products, quotients, and compositions of continuous functions are themselves continuous over their domain.


Students should already be familiar with

  • one-sided and normal limits,
  • continuity at a point,
  • the definition of a discontinuity.


Students will not cover

  • differentiability.

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