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Overview
Integrated Math II
13. CC.HSF.IF.C.8
13.9 Operations with functions
Operations with Functions
Learn how to add, subtract, multiply, and divide functions, then determine the domain of the resulting combined function with clear worked examples.
What You'll Learn
You can combine two functions using addition, subtraction, multiplication, or division, just like you combine numbers.
The rule for each combined function is found by applying the operation to the outputs, f of x and g of x, for the same input.
The domain of a sum, difference, or product is the overlap of the two original domains, while a quotient also excludes values that make the denominator zero.
Function operations are different from composition of functions, which plugs one function's output into another function.
Practicing with simple polynomial functions first makes it easier to spot domain restrictions before moving to more complex functions.
What You'll Practice
1
Adding function values from tables and graphs at specific points
2
Subtracting function outputs to find differences between two functions
3
Multiplying function values and plotting the resulting products
4
Dividing functions while identifying undefined points where division by zero occurs
Why This Matters
Operations with functions are essential for modeling real-world situations where multiple quantities interact, like combining profits, comparing rates, or analyzing compound relationships. You'll use these skills throughout algebra, precalculus, and calculus when working with complex mathematical models.
Before You Start — Make Sure You Can:
This Unit Includes
1 Video lesson
Learning resources
Skills
Function Operations
Addition of Functions
Subtraction of Functions
Multiplication of Functions
Division of Functions
Graphing Functions
Domain Restrictions
Undefined Values
OH Curriculum Aligned