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Overview
Algebra I
35. CC.HSF.IF.C.8
35.6 Subtracting functions
Subtracting Functions
Find out how to subtract two functions, combine their rules correctly, and figure out the domain of the result with clear worked examples.
What You'll Learn
Subtracting functions means creating a new function by writing (f minus g)(x) equals f(x) minus g(x).
You subtract the two output expressions and then simplify by combining like terms.
The domain of the difference function is the set of x values shared by the domains of both original functions.
Order matters, since (f minus g)(x) is generally not the same as (g minus f)(x).
Watch for a minus sign in front of a whole expression, since it must be distributed to every term inside.
What You'll Practice
1
Subtracting polynomial functions with multiple terms
2
Evaluating function differences at specific x-values algebraically
3
Reading coordinates from graphs to compute function subtraction
4
Sketching difference graphs by plotting key points and turning points
Why This Matters
Subtracting functions is essential for comparing rates of change, analyzing net effects in science and economics, and understanding how different mathematical relationships interact. This skill prepares you for calculus and advanced problem-solving across STEM fields.
Before You Start — Make Sure You Can:
This Unit Includes
6 Video lessons
Practice exercises
Learning resources
Skills
Function Operations
Function Subtraction
Polynomial Expressions
Function Evaluation
Graph Analysis
Coordinate Reading
KY Curriculum Aligned