Functions Class Lectures

The STEM concept of input and output in functions algebra refers to the relationship between two variables, where one variable (the input) is used to determine the value of another variable (the output). In this context, functions algebra involves the use of mathematical equations to describe the relationship between the input and output variables. The input variable is typically represented by the letter "x", while the output variable is represented by the letter "y". By manipulating the input variable using mathematical operations such as addition, subtraction, multiplication, and division, we can determine the corresponding value of the output variable. This concept is fundamental to many areas of STEM, including computer programming, engineering, and data analysis.

6 topics

12 Hours

Educators

Course Curriculum

Master Algebra Basics: Your Introduction to Algebra

60 videos

Mastering Linear Functions: A Comprehensive Guide

35 videos

Solve Linear Inequalities: Mastering the Art of Equation Solutions

35 videos

20 videos

Graph Linear Functions

40 videos

Write Linear Equations

45 videos

Functions Lecture Videos, Solved Step-by-Step

Functions

Function Notation - Example 1

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

Julie Silva

Functions

Function Notation - Example 2

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

Julie Silva

Functions

Function Notation - Example 3

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

Julie Silva

Functions

Function Notation - Example 4

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

Julie Silva

Functions

Function Notation - Overview

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

Julie Silva

Functions

Graphing Functions by Making a Table - Example 1

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x). The input and output of a function are often real numbers, but they can also be elements of any other set for which the relation makes sense. For instance, one can define a function from the set of integers to the set of even integers, or a function from the set of people to the set of people taller than six feet. Functions of various kinds appear in many areas of mathematics and science. There are infinitely many (algebraic) functions, such as the trigonometric functions sine and cosine, and exponential function. Functions also appear in the solutions of differential equations, in the study of differential geometry, and in many other areas of mathematics.

Julie Silva

Functions

Graphing Functions by Making a Table - Example 2

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x). The input and output of a function are often real numbers, but they can also be elements of any other set for which the relation makes sense. For instance, one can define a function from the set of integers to the set of even integers, or a function from the set of people to the set of people taller than six feet. Functions of various kinds appear in many areas of mathematics and science. There are infinitely many (algebraic) functions, such as the trigonometric functions sine and cosine, and exponential function. Functions also appear in the solutions of differential equations, in the study of differential geometry, and in many other areas of mathematics.

Julie Silva

Functions

Graphing Functions by Making a Table - Example 3

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x). The input and output of a function are often real numbers, but they can also be elements of any other set for which the relation makes sense. For instance, one can define a function from the set of integers to the set of even integers, or a function from the set of people to the set of people taller than six feet. Functions of various kinds appear in many areas of mathematics and science. There are infinitely many (algebraic) functions, such as the trigonometric functions sine and cosine, and exponential function. Functions also appear in the solutions of differential equations, in the study of differential geometry, and in many other areas of mathematics.

Julie Silva

Functions

Graphing Functions by Making a Table - Example 4

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x). The input and output of a function are often real numbers, but they can also be elements of any other set for which the relation makes sense. For instance, one can define a function from the set of integers to the set of even integers, or a function from the set of people to the set of people taller than six feet. Functions of various kinds appear in many areas of mathematics and science. There are infinitely many (algebraic) functions, such as the trigonometric functions sine and cosine, and exponential function. Functions also appear in the solutions of differential equations, in the study of differential geometry, and in many other areas of mathematics.

Julie Silva

Functions

Graphing Functions by Making a Table - Overview

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x). The input and output of a function are often real numbers, but they can also be elements of any other set for which the relation makes sense. For instance, one can define a function from the set of integers to the set of even integers, or a function from the set of people to the set of people taller than six feet. Functions of various kinds appear in many areas of mathematics and science. There are infinitely many (algebraic) functions, such as the trigonometric functions sine and cosine, and exponential function. Functions also appear in the solutions of differential equations, in the study of differential geometry, and in many other areas of mathematics.

Julie Silva

Functions

Relations and Functions - Example 1

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x). Functions of various kinds are "the central objects of investigation" in most fields of modern mathematics. There are many ways to describe or represent a function. Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input. In many other cases, a function is given by a picture, called the graph of the function. Other functions may be defined by a table that gives the outputs for selected inputs. A function could be described implicitly, for example as the inverse to another function or as a solution of a differential equation.

Julie Silva

Functions

Relations and Functions - Example 2

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x). Functions of various kinds are "the central objects of investigation" in most fields of modern mathematics. There are many ways to describe or represent a function. Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input. In many other cases, a function is given by a picture, called the graph of the function. Other functions may be defined by a table that gives the outputs for selected inputs. A function could be described implicitly, for example as the inverse to another function or as a solution of a differential equation.

Julie Silva

Functions

Relations and Functions - Example 3

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x). Functions of various kinds are "the central objects of investigation" in most fields of modern mathematics. There are many ways to describe or represent a function. Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input. In many other cases, a function is given by a picture, called the graph of the function. Other functions may be defined by a table that gives the outputs for selected inputs. A function could be described implicitly, for example as the inverse to another function or as a solution of a differential equation.

Julie Silva

Functions

Relations and Functions - Example 4

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x). Functions of various kinds are "the central objects of investigation" in most fields of modern mathematics. There are many ways to describe or represent a function. Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input. In many other cases, a function is given by a picture, called the graph of the function. Other functions may be defined by a table that gives the outputs for selected inputs. A function could be described implicitly, for example as the inverse to another function or as a solution of a differential equation.

Julie Silva

Functions

Relations and Functions - Overview

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x). Functions of various kinds are "the central objects of investigation" in most fields of modern mathematics. There are many ways to describe or represent a function. Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input. In many other cases, a function is given by a picture, called the graph of the function. Other functions may be defined by a table that gives the outputs for selected inputs. A function could be described implicitly, for example as the inverse to another function or as a solution of a differential equation.

Julie Silva

Functions

The Coordinate Plane - Example 1

In mathematics, the Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. The origin (0,0) is usually located at the center of the grid formed by the points, but in some contexts (such as graphing) it is useful to define the coordinates so that the origin is "outside" the grid, allowing the coordinates to be interpreted as relative distances from the origin. The two perpendicular axes are called the "axes" of the Cartesian coordinate system, and the points where they meet are its "intercepts". The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.

Julie Silva

Functions

The Coordinate Plane - Example 2

In mathematics, the Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. The origin (0,0) is usually located at the center of the grid formed by the points, but in some contexts (such as graphing) it is useful to define the coordinates so that the origin is "outside" the grid, allowing the coordinates to be interpreted as relative distances from the origin. The two perpendicular axes are called the "axes" of the Cartesian coordinate system, and the points where they meet are its "intercepts". The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.

Julie Silva

Functions

The Coordinate Plane - Example 3

In mathematics, the Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. The origin (0,0) is usually located at the center of the grid formed by the points, but in some contexts (such as graphing) it is useful to define the coordinates so that the origin is "outside" the grid, allowing the coordinates to be interpreted as relative distances from the origin. The two perpendicular axes are called the "axes" of the Cartesian coordinate system, and the points where they meet are its "intercepts". The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.

Julie Silva

Functions

The Coordinate Plane - Example 4

In mathematics, the Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. The origin (0,0) is usually located at the center of the grid formed by the points, but in some contexts (such as graphing) it is useful to define the coordinates so that the origin is "outside" the grid, allowing the coordinates to be interpreted as relative distances from the origin. The two perpendicular axes are called the "axes" of the Cartesian coordinate system, and the points where they meet are its "intercepts". The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.

Julie Silva

Functions

The Coordinate Plane - Overview

In mathematics, the Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. The origin (0,0) is usually located at the center of the grid formed by the points, but in some contexts (such as graphing) it is useful to define the coordinates so that the origin is "outside" the grid, allowing the coordinates to be interpreted as relative distances from the origin. The two perpendicular axes are called the "axes" of the Cartesian coordinate system, and the points where they meet are its "intercepts". The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.

Julie Silva