Topic
My Progress
Pug Score
0%
Study Points
+0
Overview
Watch
Read
Next Steps
Adaptive practice
Video lessons
Overview
Watch
Read
Next Steps
Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
C. Polynomial and Rational Functions
36. 12AF.C2.2
36.1 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
ON Curriculum Aligned