4-6 Formalizing Relations and Functions
Objectives
To determine whether a relation is a function
To find domain and range and use function notation
Dynamic Activity
Function Explorer
A relation is a pairing of numbers in one set, called the domain, with numbers in another set, called the range. A relation is often represented as a set of ordered pairs (x, y). In this case, the domain is the set of x-values and the range is the set of y-values.
Lesson Vocabulary
- relation
- domain
- range
- vertical line test
- function notation
Essential Understanding A function is a special type of relation in which each value in the domain is paired with exactly one value in the range.
Problem 1 Identifying Functions Using Mapping Diagrams
Identify the domain and range of each relation. Represent the relation with a mapping diagram. Is the relation a function?
Think
When is a relation not a function?
A function maps each domain value to exactly one range value. So a relation that maps a domain value to more than one range value cannot be a function.
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{(
The domain is {
The range is {0.5, 2.5, 6.5}.
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{(6, 5), (4, 3), (6, 4), (5, 8)}
The domain is {4, 5, 6}.
The range is {3, 4, 5, 8}.
Table of Contents
- 2-1 and 2-2 Solving One- and Two-Step Equations
- 2-3 Solving Multi-Step Equations
- 2-4 Solving Equations With Variables on Both Sides
- 2-5 Literal Equations and Formulas
- 2-6 Ratios, Rates, and Conversions
- 2-7 and 2-8 Solving Proportions and Using Similar Figures
- 2-9 Percents
- 2-10 Change Expressed as a Percent
- 3-1 Inequalities and Their Graphs
- 3-2 Solving Inequalities Using Addition or Subtraction
- 3-3 Solving Inequalities Using Multiplication or Division
- 3-4 Solving Multi-Step Inequalities
- 3-5 Working With Sets
- 3-6 Compound Inequalities
- 3-7 Absolute Value Equations and Inequalities
- 3-8 Unions and Intersections of Sets
- Chapter 1 Foundations for Algebra
- Chapter 2 Solving Equations
- Chapter 3 Solving Inequalities
- Chapter 4 An Introduction to Functions
- Chapter 5 Linear Functions
- Chapter 6 Systems of Equations and Inequalities
- Chapter 7 Exponents and Exponential Functions
- Chapter 8 Polynomials and Factoring
- Chapter 9 Quadratic Functions and Equations
- Chapter 10 Radical Expressions and Equations
- Chapter 11 Rational Expressions and Functions
- Chapter 12 Data Analysis and Probability