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
- 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