Overview
Watch
Read
Next Steps
Overview
Mathematics 30-1
20. Graph and analyze rational functions
20.1 What is a rational function?
What Is a Rational Function?
One polynomial divided by another -- any x that makes the denominator zero is excluded from the domain.
What You'll Learn
A rational function is one polynomial divided by another: f(x) = p(x)/q(x).
Any x that makes the denominator zero is excluded from the domain.
f(x) = 1/x is the simplest example, undefined at x = 0.
1/x has two branches, split by a vertical asymptote at x=0 and horizontal at y=0.
An excluded value creates either a removable hole or a true vertical asymptote.
What You'll Practice
1
Creating tables of values to plot rational function graphs
2
Finding non-permissible values from denominator restrictions
3
Identifying vertical and horizontal asymptotes from functions
4
Analyzing left-hand and right-hand behavior as x approaches infinity
Why This Matters
Rational functions appear everywhere in advanced math and real applications, from rates and ratios to physics formulas. Understanding asymptotes and non-permissible values is essential for calculus, where you'll analyze limits and continuity of complex functions.
This Unit Includes
1 Video lesson
Learning resources
Skills
Rational Functions
Asymptotes
Non-permissible Values
Polynomials
Graphing
End Behavior
Domain Restrictions
AB Curriculum Aligned