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Chapter 12.6
Point of discontinuity
What You'll Learn
Identify points of discontinuity in rational functions by finding common factors
Distinguish between points of discontinuity and vertical asymptotes
Simplify rational expressions by factoring and canceling common terms
Calculate coordinates of discontinuity points using simplified expressions
Recognize that denominator restrictions create non-permissible values
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
Skills
Rational Functions
Discontinuity
Factoring
Synthetic Division
Non-permissible Values
Asymptotes
Simplifying Expressions
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