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Discrete Mathematics/Computer Science
13. CC.HSF.IF.B.5
13.1 Point of discontinuity
Point of Discontinuity
A removable discontinuity is a hole: the function simplifies to a clean expression but stays undefined at one x-value.
What You'll Learn
A removable discontinuity is a hole: the function simplifies but stays undefined there.
Example: (x squared - 4)/(x-2) simplifies to x+2, with a hole at (2, 4).
Find one by factoring the numerator and denominator and canceling shared factors.
The hole's y-coordinate comes from the simplified expression, not the original.
If the factor doesn't cancel, it's a true vertical asymptote instead of a hole.
What You'll Practice
1
Factoring polynomials in numerator and denominator using synthetic division
2
Finding non-permissible values from factored denominators
3
Identifying and plotting hollow points on rational function graphs
4
Computing y-coordinates by substituting x-values into simplified forms
Why This Matters
Understanding points of discontinuity helps you graph rational functions accurately and avoid undefined values. This concept is essential for calculus, where you'll analyze limits and continuity, and it sharpens your ability to work with complex algebraic expressions.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Practice exercises
Learning resources
Skills
Rational Functions
Discontinuity
Factoring
Synthetic Division
Non-permissible Values
Asymptotes
Simplifying Expressions
OH Curriculum Aligned