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Overview
Algebra I
31. CA.A1.F.IF.8
31.5 Dividing functions
Dividing Functions
Dividing functions forms the quotient of two functions, defined everywhere the divisor function is not zero.
What You'll Learn
Dividing functions forms the quotient (f/g)(x) = f(x) divided by g(x).
Evaluate at a point by dividing the two output values.
The quotient is undefined wherever the divisor g(x) equals zero.
Exclude every x with g(x) = 0 from the domain, even after simplifying.
Simplify by factoring and cancelling, then state the domain restriction.
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
Learning resources
Skills
Function Division
Rational Functions
Domain Restrictions
Factoring
Simplification
Discontinuity
Vertical Asymptotes
CA Curriculum Aligned