Functions

This course introduces functions which are the most common type of mathematical formula. It discusses the terms: average rate of change, continuity of a function, domain, range, extreme intervals of increase and decrease, operation of functions, inverse function. It covers the use of the function notation. It also provides a detailed discussion about one-to-one and inverse functions. It also explains in words why a given function is a function or why it does not have an inverse. It also discusses different kinds of functions as power function, piecewise function, It explains the transformation of graphs of different functions.

15 topics

337 lectures

Educators

LL

Course Curriculum

40 videos

Powers and Polynomial

25 videos

Rational Numbers

11 videos

41 videos

Exponential Functions

15 videos

61 videos

Parametric Equations

5 videos

Introduction to Vectors

15 videos

15 videos

Polar Coordinates

5 videos

30 videos

Introduction to Conic Sections

23 videos

15 videos

Introduction to Combinatorics and Probability

16 videos

Introduction to Sequences and Series

20 videos

Functions Lectures

Functions

Continuity - Overview

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output. Otherwise, a function is said to be a discontinuous function.

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Functions

Continuity - Example 1

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output. Otherwise, a function is said to be a discontinuous function.

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Functions

Continuity - Example 2

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output. Otherwise, a function is said to be a discontinuous function.

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Functions

Continuity - Example 3

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output. Otherwise, a function is said to be a discontinuous function.

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Functions

Continuity - Example 4

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output. Otherwise, a function is said to be a discontinuous function.

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Functions

Extrema Intervals of Increase Deacrease - Overview

In mathematics, the maximum and minimum of a function are its most extreme values. The value of a function at a maximum (minimum) is called the maximum (minimum) value of the function. The maximum value of a function may be "infinite", either +? or ??. The minimum value of a function may be "negative infinity" or "positive infinity".

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Functions

Extrema Intervals Of Increase or Decrease - Example 1

In mathematics, the infimum and supremum of a subset of a metric space are the greatest and least elements, respectively, of the set. It is relevant to the concept of minimum and maximum value but, it would distinguish the special sets which have no minimum or maximum.

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Functions

Extrema Intervals Of Increase or Decrease - Example 2

In mathematics, the infimum and supremum of a subset of a metric space are the greatest and least elements, respectively, of the set. It is relevant to the concept of minimum and maximum value but, it would distinguish the special sets which have no minimum or maximum.

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Functions

Extrema Intervals Of Increase or Decrease - Example 3

In mathematics, the infimum and supremum of a subset of a metric space are the greatest and least elements, respectively, of the set. It is relevant to the concept of minimum and maximum value but, it would distinguish the special sets which have no minimum or maximum.

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Functions

Extrema Intervals Of Increase or Decrease - Example 4

In mathematics, the infimum and supremum of a subset of a metric space are the greatest and least elements, respectively, of the set. It is relevant to the concept of minimum and maximum value but, it would distinguish the special sets which have no minimum or maximum.

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Functions

Power Functions - Overview

In mathematics, a power function is a function in which the independent variable is the exponent of the dependent variable.

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Functions

Power Functions - Example 1

In mathematics, a power function is a function in which the independent variable is the exponent of the dependent variable.

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Functions

Power Functions - Example 2

In mathematics, a power function is a function in which the independent variable is the exponent of the dependent variable.

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Functions

Power Functions - Example 3

In mathematics, a power function is a function in which the independent variable is the exponent of the dependent variable.

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Functions

Power Functions - Example 4

In mathematics, a power function is a function in which the independent variable is the exponent of the dependent variable.

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Functions

Average Rate Of Change - Overview

The average rate of change of a quantity is the ratio of the change to the value of the quantity. In mathematical analysis, it is a type of differential. The average rate of change of a function is the derivative of the function.

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Functions

Average Rate Of Change - Example 1

The average rate of change of a quantity is the ratio of the change to the value of the quantity. In mathematical analysis, it is a type of differential. The average rate of change of a function is the derivative of the function.

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Functions

Average Rate Of Change - Example 2

The average rate of change of a quantity is the ratio of the change to the value of the quantity. In mathematical analysis, it is a type of differential. The average rate of change of a function is the derivative of the function.

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Functions

Average Rate Of Change - Example 3

The average rate of change of a quantity is the ratio of the change to the value of the quantity. In mathematical analysis, it is a type of differential. The average rate of change of a function is the derivative of the function.

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Functions

Average Rate Of Change - Example 4

The average rate of change of a quantity is the ratio of the change to the value of the quantity. In mathematical analysis, it is a type of differential. The average rate of change of a function is the derivative of the function.

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Functions

Transformations Of Graphs - 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) (read "f of x", "f at x", or "f(x) of x"). In this example, if the input is ?3, then the output is 9, and we may write f(?3) = 9.

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Functions

Transformations Of Graphs - 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) (read "f of x", "f at x", or "f(x) of x"). In this example, if the input is ?3, then the output is 9, and we may write f(?3) = 9.

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Functions

Transformations Of Graphs - 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) (read "f of x", "f at x", or "f(x) of x"). In this example, if the input is ?3, then the output is 9, and we may write f(?3) = 9.

Lily An

Functions

Transformations Of Graphs - 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) (read "f of x", "f at x", or "f(x) of x"). In this example, if the input is ?3, then the output is 9, and we may write f(?3) = 9.

Lily An

Functions

Transformations Of Graphs - 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) (read "f of x", "f at x", or "f(x) of x"). In this example, if the input is ?3, then the output is 9, and we may write f(?3) = 9.

Lily An

Functions

Piecewise Functions - Overview

In mathematics, a piecewise function is a function that is defined by multiple conditions. The function is defined separately for each set of conditions. The function is not defined at the points where the conditions are not met.

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Functions

Piecewise Functions - Example 1

In mathematics, a piecewise function is a function that is defined by multiple conditions. The function is defined separately for each set of conditions. The function is not defined at the points where the conditions are not met.

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Functions

Piecewise Functions - Example 2

In mathematics, a piecewise function is a function that is defined by multiple conditions. The function is defined separately for each set of conditions. The function is not defined at the points where the conditions are not met.

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Functions

Piecewise Functions - Example 3

In mathematics, a piecewise function is a function that is defined by multiple conditions. The function is defined separately for each set of conditions. The function is not defined at the points where the conditions are not met.

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Functions

Piecewise Functions - Example 4

In mathematics, a piecewise function is a function that is defined by multiple conditions. The function is defined separately for each set of conditions. The function is not defined at the points where the conditions are not met.

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Functions

Operations - Overview

In mathematics, an operation on a mathematical object is a rule which combines two or more mathematical objects (usually numbers, vectors, or matrices) to produce a third object. Operations can be used to model physical processes, like addition in physics.

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Functions

Operations - Example 1

In mathematics, an operation on a mathematical object is a rule which combines two or more mathematical objects (usually numbers, vectors, or matrices) to produce a third object. Operations can be used to model physical processes, like addition in physics.

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Functions

Operations - Example 2

In mathematics, an operation on a mathematical object is a rule which combines two or more mathematical objects (usually numbers, vectors, or matrices) to produce a third object. Operations can be used to model physical processes, like addition in physics.

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Functions

Operations - Example 3

In mathematics, an operation on a mathematical object is a rule which combines two or more mathematical objects (usually numbers, vectors, or matrices) to produce a third object. Operations can be used to model physical processes, like addition in physics.

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Functions

Operations - Example 4

In mathematics, an operation on a mathematical object is a rule which combines two or more mathematical objects (usually numbers, vectors, or matrices) to produce a third object. Operations can be used to model physical processes, like addition in physics.

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Functions

Inverses - Overview

In mathematics, the concept of inverse functions arises from the study of one-to-one correspondence. In the mathematical definition of function, a function "f" is said to be an inverse function of a function "g" if the image of every element of the domain of "g" is the image of some element of the codomain of "f". In other words, "f" is the inverse of "g" if, for each "x" in the domain of "g", there is a unique "y" in the codomain of "f" such that "g"("y") = "x".

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Functions

Inverses - Example 1

In mathematics, the concept of inverse functions arises from the study of one-to-one correspondence. In the mathematical definition of function, a function "f" is said to be an inverse function of a function "g" if the image of every element of the domain of "g" is the image of some element of the codomain of "f". In other words, "f" is the inverse of "g" if, for each "x" in the domain of "g", there is a unique "y" in the codomain of "f" such that "g"("y") = "x".

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Functions

Inverses - Example 2

In mathematics, the concept of inverse functions arises from the study of one-to-one correspondence. In the mathematical definition of function, a function "f" is said to be an inverse function of a function "g" if the image of every element of the domain of "g" is the image of some element of the codomain of "f". In other words, "f" is the inverse of "g" if, for each "x" in the domain of "g", there is a unique "y" in the codomain of "f" such that "g"("y") = "x".

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Functions

Inverses - Example 3

In mathematics, the concept of inverse functions arises from the study of one-to-one correspondence. In the mathematical definition of function, a function "f" is said to be an inverse function of a function "g" if the image of every element of the domain of "g" is the image of some element of the codomain of "f". In other words, "f" is the inverse of "g" if, for each "x" in the domain of "g", there is a unique "y" in the codomain of "f" such that "g"("y") = "x".

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Functions

Inverses - Example 4

In mathematics, the concept of inverse functions arises from the study of one-to-one correspondence. In the mathematical definition of function, a function "f" is said to be an inverse function of a function "g" if the image of every element of the domain of "g" is the image of some element of the codomain of "f". In other words, "f" is the inverse of "g" if, for each "x" in the domain of "g", there is a unique "y" in the codomain of "f" such that "g"("y") = "x".

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