mathleaks.com mathleaks.com Start chapters home Start History history History expand_more Community
Community expand_more
menu_open Close
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
Expand menu menu_open home
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open
article Article
menu_book Textbook Solutions
school eCourses
question_answer Community
description Worksheets
calculate Math Solver
arrow_back arrow_forward

Concept

Function

A function is a relation in which each input value corresponds to exactly one output value. The set of all possible input values is called the domain. Conversely, the set of all possible output values is called the range. If represents the inputs and the outputs of a function, it is often said that is a function of This way of representing the dependent variable is called function notation. A function can be represented using a table, a mapping diagram, an equation, or a graph.
representations of functions

Note that every function is a relation, but not every relation is a function. In the applet below, Relation I is a function because each input value in the domain is paired with only one output value in the range. However, Relation II is not a function because is paired with two output values in the range.

There are different ways to determine whether or not a relation is a function. The way the relation is represented can help to decide how to check whether or not it is a function.

  • If the relation is given as a set of coordinates, a table or mapping diagram could be helpful.
  • If the relation is given as a graph, the Vertical Line Test can be used.

{{ 'ml-article-textbook-solutions-heading' | message }}

{{ 'ml-article-textbook-solutions-description' | message }}

{{ 'ml-article-textbook-solutions-expert-solutions' | message }}

{{ 'ml-article-textbook-solutions-math-solver-scanner' | message }}

{{ 'ml-article-textbook-solutions-answers-hints-steps' | message }}

{{ 'ml-article-ecourses-heading' | message }}

{{ 'ml-article-ecourses-description' | message }}

{{ 'ml-article-ecourses-interactive' | message }}

{{ 'ml-article-ecourses-chapter-tests' | message }}

{{ 'ml-article-ecourses-exercise-levels' | message }}

{{ 'ml-article-ecourses-rank-stats' | message }}

{{ 'ml-article-ecourses-video-lessons' | message }}

{{ 'ml-article-ecourses-course-theory' | message }}

{{ 'ml-article-ecourses-join-classroom' | message }}

{{ 'ml-article-ecourses-graphing-calculator' | message }}

{{ 'ml-article-ecourses-quiz-games' | message }}

{{ 'ml-article-ecourses-study-together' | message }}

{{ 'ml-article-community-heading' | message }}

{{ 'ml-article-community-description' | message }}

{{ 'ml-article-community-create-and-share-channels' | message }}

{{ 'ml-article-community-share-content-and-challenge' | message }}

{{ 'ml-article-community-cooperate-with-friends' | message }}

{{ 'ml-article-worksheets-heading' | message }}

{{ 'ml-article-worksheets-description' | message }}

{{ 'ml-article-worksheets-course1' | message }}

{{ 'ml-article-worksheets-course2' | message }}

{{ 'ml-article-worksheets-course3' | message }}

{{ 'ml-article-worksheets-course4' | message }}

{{ 'ml-article-math-solver-heading' | message }}

{{ 'ml-article-math-solver-description' | message }}

{{ 'ml-article-math-solver-photo-scan-solve' | message }}

{{ 'ml-article-math-solver-step-by-step' | message }}

{{ 'ml-article-math-solver-graph-math-problem' | message }}