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Mathematics 11
Relations and Functions
13. Demonstrate understanding of characteristics of quadratic functions
13.9 Adding functions
Adding Functions
A clear, step-by-step guide to adding functions, including polynomial and rational functions, with worked examples and domain checks.
What You'll Learn
Adding functions means combining their outputs using the rule (f+g)(x) equals f(x) plus g(x).
To add polynomial functions, combine like terms after substituting the expressions for f(x) and g(x).
To add rational functions, find a common denominator first, just like adding fractions.
The domain of a sum of functions is the overlap (intersection) of the domains of the original functions.
Checking the domain matters most when rational functions are involved, since denominators cannot equal zero.
What You'll Practice
1
Adding polynomial expressions with multiple variable terms
2
Evaluating function sums at given x-values using substitution
3
Graphing the sum of two functions using important points
4
Simplifying expressions involving function addition and scalar multiplication
Why This Matters
Adding functions is essential for modeling combined real-world quantities like total profit, combined forces, or mixed costs. You'll use this skill throughout algebra, precalculus, and calculus when working with complex systems that involve multiple changing quantities.
Before You Start — Make Sure You Can:
This Unit Includes
6 Video lessons
Practice exercises
Learning resources
Skills
Function Addition
Function Notation
Polynomials
Like Terms
Function Evaluation
Graphing Functions
Algebraic Simplification
NS Curriculum Aligned