---
title: Functions
description: Functions are mathematical relations that associate each input from a domain with exactly one output in a codomain. Learners will understand function notation, domain and range, composition, and inverses to model and analyze mathematical relationships.
category: mathematics
subcategory: algebra
difficulty: beginner, intermediate, advanced
url: /subject/algebra-functions
---

# Functions

Functions are mathematical relations that associate each input from a domain with exactly one output in a codomain. Learners will understand function notation, domain and range, composition, and inverses to model and analyze mathematical relationships.

## Available Resources

2 Books • 2 Courses • 2 Websites

## Websites

### 1. Khan Academy Functions

Algebra I unit of video lessons and graded practice on function notation, domain and range, graph interpretation, and inverse functions. Progress is tracked per skill, so learners can identify which specific ideas still fail.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions

**Tags:** algebra, functions, domain-and-range, graphing, practice-problems

### 2. mathsisfun.com

MathIsFun.com is a beginner-friendly math site that explains concepts with clear, step-by-step lessons and interactive activities. It covers topics from algebra and linear equations to geometry, fractions, data, and more, with practice problems, worksheets, and quizzes.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathsisfun.com

**Tags:** websites, mathematics-statistics, algebra

## Courses

### 1. Algebra 1

**Author:** Sal Khan

Complete school Algebra 1 course of video lessons and graded practice covering linear equations and inequalities, graphing, functions, systems of equations, exponents, polynomials and quadratics. Learners finish able to solve and graph linear and quadratic problems and read function notation.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://www.khanacademy.org/math/algebra

**Tags:** algebra, linear-equations, functions, systems-of-equations, quadratic-equations

### 2. Algebra: Elementary to Advanced - Polynomials and Roots

**Author:** Joseph W. Cutrone

Third course in Johns Hopkins's algebra sequence, covering exponential functions, polynomial arithmetic and factoring, square and nth roots, and percent and interest applications. Finishes with a cumulative exam, preparing you for precalculus, statistics or data science coursework.

**Difficulty:** Beginner | **Language:** English | **Price:** Free

**Link:** https://www.coursera.org/learn/polynomials-roots

**Tags:** polynomials, factoring, exponents, radicals, algebra

## Books

### 1. Precalculus: Mathematics for Calculus

**Author:** James Stewart, Lothar Redlin, Saleem Watson

Widely used college precalculus textbook covering algebra review, functions and their graphs, polynomial, rational, exponential and logarithmic functions, trigonometry, systems of equations, conic sections and limits. Prepares students to handle the algebraic and graphical function work that calculus assumes.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/053437610X?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, algebra

### 2. Functions and Graphs

**Author:** I. M. Gelfand, E. G. Glagoleva, E. E. Shnol

Short problem-driven book from Gelfand's Moscow correspondence school that teaches high-school students to sketch graphs of linear, quadratic, fractional-linear and other functions by reasoning about transformations, symmetry and behavior rather than plotting points. Builds lasting intuition for how formulas shape graphs.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/0486425649?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, algebra

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