Chapter 10.8
Dividing functions
What You'll Learn
Write division of functions as a quotient of two expressions
Identify domain restrictions by setting denominators not equal to zero
Simplify rational expressions by factoring and canceling common terms
Distinguish between vertical asymptotes and points of discontinuity
Evaluate division of functions at specific x-values
What You'll Practice
1
Dividing polynomial and rational functions with proper domain notation
2
Factoring numerators and denominators before simplifying quotients
3
Finding domain restrictions including hidden discontinuities
4
Sketching graphs of rational functions with asymptotes and holes
Why This Matters
Dividing functions is essential for understanding rational expressions, which appear throughout calculus, physics, and engineering. Mastering domain restrictions prevents undefined values and helps you analyze asymptotic behavior in real-world models like rates, ratios, and optimization problems.
Before You Start — Make Sure You Can:
This Unit Includes
9 Video lessons
Practice exercises
Skills
Function Division
Rational Functions
Domain Restrictions
Factoring
Simplification
Discontinuity
Vertical Asymptotes
OH Curriculum Aligned
