# 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.

#### 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.