Difference between revisions of "Functions"
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==Introduction== | ==Introduction== | ||
| − | A relation is a set of | + | A relation is a set of input values and output values, often written as an ordered pair of the form (input, output). A function is a relation in which each possible input value leads to exactly one output value. The input values make up the [[Domain of a Function]], and the output values make up the [[Range of a Function]], also known as the codomain. A relation is NOT a function if one input in the domain maps to multiple outputs in the range. For example, consider the following relations: R1 = {(1,2), (1, 3), (2, 4), (3, 5)} and R2 = {(1,2), (2, 4), (3, 5), (4, 5)}. The relation R1 is not a function because the input 1 maps to both 2 and 3. However, the relation R2 is a function since each input only maps to one output. Note that multiple inputs can map to a single output; that is, R2 is still a function despite the fact that the inputs 3 and 4 both mapping to the same output, 5. If a function maps each input to a distinct output (that is, no two inputs lead to the same output), we say that the function is "one-to-one" or "injective". |
==Resources== | ==Resources== | ||
| + | * [https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:evaluating-functions/v/what-is-a-function What is a Function?], Khan Academy | ||
* [https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/determine-whether-a-relation-represents-a-function/ Determining if a Relation is a Function], Lumen Learning | * [https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/determine-whether-a-relation-represents-a-function/ Determining if a Relation is a Function], Lumen Learning | ||
* [https://www.cliffsnotes.com/study-guides/calculus/precalculus/functions/relations-vs-functions Relations vs. Functions], Cliff's Notes | * [https://www.cliffsnotes.com/study-guides/calculus/precalculus/functions/relations-vs-functions Relations vs. Functions], Cliff's Notes | ||
* [https://courses.lumenlearning.com/waymakercollegealgebra/chapter/identify-functions-using-graphs/ Identifying Functions Using Graphs], Lumen Learning | * [https://courses.lumenlearning.com/waymakercollegealgebra/chapter/identify-functions-using-graphs/ Identifying Functions Using Graphs], Lumen Learning | ||
Revision as of 11:35, 15 September 2021
Introduction
A relation is a set of input values and output values, often written as an ordered pair of the form (input, output). A function is a relation in which each possible input value leads to exactly one output value. The input values make up the Domain of a Function, and the output values make up the Range of a Function, also known as the codomain. A relation is NOT a function if one input in the domain maps to multiple outputs in the range. For example, consider the following relations: R1 = {(1,2), (1, 3), (2, 4), (3, 5)} and R2 = {(1,2), (2, 4), (3, 5), (4, 5)}. The relation R1 is not a function because the input 1 maps to both 2 and 3. However, the relation R2 is a function since each input only maps to one output. Note that multiple inputs can map to a single output; that is, R2 is still a function despite the fact that the inputs 3 and 4 both mapping to the same output, 5. If a function maps each input to a distinct output (that is, no two inputs lead to the same output), we say that the function is "one-to-one" or "injective".
Resources
- What is a Function?, Khan Academy
- Determining if a Relation is a Function, Lumen Learning
- Relations vs. Functions, Cliff's Notes
- Identifying Functions Using Graphs, Lumen Learning
