Lesson: Continuity of Functions Mathematics

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In this lesson, we will learn how to check the continuity of a function over its domain and determine the interval on which it is continuous.

Lesson Plan

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.