Lesson: Classifying Discontinuities Mathematics • 12th Grade

In this lesson, we will learn how to differentiate between the three types of function discontinuity at a given point.

Lesson Plan

Students will be able to

know what it means for a function to have a discontinuity at a point,
classify function discontinuities as removable, essential, or jump discontinuities,
recognize infinite discontinuities by looking for vertical asymptotes.

Q1:

Consider the function

What is ?

What type of discontinuity does the function have at ?

Q2:

Consider the function

What is ?

What type of discontinuity does the function have at ?

Q3:

Consider the function .

Find the type of discontinuity that the function has at , if it has any.