Students will learn how to find all the discontinuities of a rational function, and classify each discontinuity as a hole or asymptote.
Watch these videos:
- Discontinuity: The Four Types of Discontinuities You Need to Know by BriTheMathGuy
- The Discontinuities - A New Netflix Series! by Raelene Maths
Have students determine what type of discontinuity a function has, given the function's definition. For example, what type of discontinuity does \(f(x) = (x - 3)/(x - 3)\) have?
Conclude by giving your students these challenges:
In the figure below, the radius of the smallest circle is \(1.\) What is the radius of the largest circle?
Here's the solution.