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HomeHomework HelpmathematicsRelations and Functions

Relations and Functions

A concept in mathematics that describes the relationships between sets, including the definition of a relation, the domain and range of a relation, and the properties of relations such as reflexivity, symmetry, and transitivity, as well as the concept of functions as a special type of relation

beginner
2 hours
Mathematics
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Overview

Relations and functions are fundamental concepts in mathematics that help us understand how different quantities relate to each other. A relation is simply a set of ordered pairs, while a function is a special type of relation where each input corresponds to exactly one output. This distinction is c...

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Key Terms

Relation
A set of ordered pairs.

Example: R = {(1, 2), (3, 4)}

Function
A relation where each input has exactly one output.

Example: f(x) = x + 1

Domain
The set of all possible input values for a function.

Example: For f(x) = x², the domain is all real numbers.

Range
The set of all possible output values of a function.

Example: For f(x) = x², the range is all non-negative real numbers.

Ordered Pair
A pair of numbers used to represent a point in a coordinate system.

Example: (3, 5)

Linear Function
A function that graphs to a straight line.

Example: f(x) = 2x + 3

Related Topics

Graphing Functions
Learn how to graph different types of functions and understand their shapes.
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Inverse Functions
Explore how to find the inverse of a function and its significance.
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Composite Functions
Understand how to combine functions to create composite functions.
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Key Concepts

Ordered PairsDomain and RangeFunction NotationTypes of Functions