Functions and Graphs resources

IPOD VIDEO: A function is a rule which operates on one number to give another number. However, not every rule describes a valid function. This unit explains how to see whether a given rule describes a valid function, and introduces some of the mathematical terms associated with functions. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

IPOD VIDEO: A function is a rule which operates on one number to give another number. However, not every rule describes a valid function. This unit explains how to see whether a given rule describes a valid function, and introduces some of the mathematical terms associated with functions. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

IPOD VIDEO: A function is a rule which operates on one number to give another number. However, not every rule describes a valid function. This unit explains how to see whether a given rule describes a valid function, and introduces some of the mathematical terms associated with functions. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

We can build up complicated functions from simple functions by using the process of composition, where the output of one function becomes the input of another. It is also sometimes necessary to carry out the reverse process, decomposing a complicated function into two or more simple functions. This unit explains how.

The hyperbolic functions have similar names to the trigonmetric functions, but they are defined in terms of the exponential function. In this unit we define the three main hyperbolic functions, and sketch their graphs. We also discuss some identities relating these functions, and mention their inverse functions and reciprocal functions.

An inverse function is a second function which undoes the work of the first one. In this unit we describe two methods for finding inverse functions, and we also explain that the domain of a function may need to be restricted before an inverse function can exist.

Some of the most important functions are linear. This unit describes how to recognize a linear function, and how to find the slope and the y-intercept of its graph.

The sine, cosine and tangent of an angle are all defined in terms of trigonometry, but they can also be expressed as functions. In this unit we examine these functions and their graphs. We also see how to restrict the domain of each function in order to define an inverse function.

Five questions on trigonometry. The first involves determining the quadrant an angle lies in, the remaining questions involve solving trigonometric equations. DEWIS resources have been made available under a Creative Commons licence by Rhys Gwynllyw & Karen Henderson, University of the West of England, Bristol.

We can build up complicated functions from simple functions by using the process of composition, where the output of one function becomes the input of another. It is also sometimes necessary to carry out the reverse process, decomposing a complicated function into two or more simple functions. This unit explains how. (Mathtutor Video Tutorial) This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

The hyperbolic functions have similar names to the trigonmetric functions, but they are defined in terms of the exponential function. In this unit we define the three main hyperbolic functions, and sketch their graphs. We also discuss some identities relating these functions, and mention their inverse functions and reciprocal functions. (Mathtutor Video Tutorial) This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

A function is a rule which operates on one number to give another number. However, not every rule describes a valid function. This unit explains how to see whether a given rule describes a valid function, and introduces some of the mathematical terms associated with functions. (Mathtutor Video Tutorial) This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

In this unit, we explain what it means for a function to tend to infinity, to minus infinity, or to a real limit, as x tends to infinity or to minus infinity. We also explain what it means for a function to tend to a real limit as x tends to a given real number. In each case, we give an example of a function that does not tend to a limit at all. (Mathtutor Video Tutorial) This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Many common functions are polynomial functions. In this unit we describe polynomial functions and look at some of their properties. (Mathtutor Video Tutorial) This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.