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Overview
Graphs of rational functions
What You'll Learn
Determine vertical asymptotes by setting the denominator equal to zero
Identify horizontal asymptotes by comparing degrees of numerator and denominator
Recognize points of discontinuity by factoring and simplifying rational functions
Find slant asymptotes using long or synthetic division when the numerator's degree exceeds the denominator's by one
Sketch rational function graphs using asymptotes, intercepts, and end behavior
What You'll Practice
1
Finding vertical and horizontal asymptotes for various rational functions
2
Factoring polynomials to identify points of discontinuity
3
Using synthetic and long division to determine slant asymptote equations
4
Plotting rational functions by combining asymptotes with intercepts and test points
Why This Matters
Graphing rational functions is essential for modeling real-world phenomena like rates, concentrations, and optimization problems. Mastering asymptotes helps you predict function behavior at extreme values and understand limits, which is foundational for calculus and advanced mathematics.
This Unit Includes
14 Video lessons
Practice exercises
Skills
Rational Functions
Vertical Asymptotes
Horizontal Asymptotes
Slant Asymptotes
Discontinuity
Factoring
Graphing
Polynomial Division
OH Curriculum Aligned