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Lesson Plan: Continuity of Functions Mathematics • Second Year of Secondary School
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.
Objectives
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.
Prerequisites
Students should already be familiar with
- one-sided and normal limits,
- continuity at a point,
- the definition of a discontinuity.
Exclusions
Students will not cover
- differentiability.
