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Multiplying Functions
Discover how to multiply two functions together, simplify the result, and figure out the domain of the new product function.
What You'll Learn
Multiplying functions means finding a new function whose output at any x is f(x) times g(x).
The notation is written as (f times g)(x), and it equals f(x) times g(x) after substituting the same input into both functions.
The domain of a product function is the overlap (intersection) of the domains of the original two functions.
Multiplying polynomial functions works just like multiplying polynomial expressions, using distribution or the FOIL pattern.
Multiplying rational functions follows the same rule but requires extra care with values that make a denominator zero.
What You'll Practice
1
Expanding products of functions involving radicals and polynomials
2
Evaluating function products at specific values using direct substitution
3
Graphing products of piecewise functions using table values
4
Identifying curves vs. straight lines in product graphs
Why This Matters
Multiplying functions is essential for modeling complex real-world scenarios where multiple relationships interact. You'll use this skill throughout calculus when working with derivatives and integrals, and it's crucial for understanding composite systems in physics, economics, and engineering.
Before You Start — Make Sure You Can:
This Unit Includes
3 Video lessons
Practice exercises
Learning resources
Skills
Function Multiplication
Function Notation
Expanding Expressions
Radicals
Graphing Functions
Piecewise Functions
Quadratic Functions
ON Curriculum Aligned