Inverse Functions and Graphs

**Graphs and Functions**

The function is a central idea in mathematics and these resources introduce the basic language and definitions of functions.

These resources explain the idea of an inverse function and, if possible, how they can be found. They also explore the connection between functions and graphs.

These resources expand the idea of a function further. They explain functions in terms of a machine and how the inputs and outputs work.

Even with the advent of computer programs, being able to plot a graph by hand is still an important skill to have. These resources explain all the parts of a graph and give advice about plotting.

Functions

Inverse Functions and Graphs Webcast

Click on the rectangle to open the Inverse Functions and Graphs Study Guide

Using Functions Webcast

Click on the rectangle to open the Using Functions Study Guide

Click on the rectangle to open the Using Functions Model Answers

Click on the rectangle to open the Using Functions Worksheet

Functions Webcast

Click on the rectangle to open the Functions Model Answers

Click on the rectangle to open the Functions

Study Guide

Click on the rectangle to open the Functions Worksheet

Plotting a Graph by Hand Webcast

Plotting a Graph by Hand

Click on the rectangle to open the Plotting a Graph by Hand Study Guide

Using This Mind Map

Click on the rectangle below to open a document to help you get the most out of this Mind Map

https://portal.uea.ac.uk/documents/6207125/8124756/Interactive+mind+map+guide.pdf/0e299529-fe1a-4c31-8675-bb29564d5a99

More Complicated Functions Webcast

Click on the rectangle to open the More Complicated Functions Study Guide

Click on the rectangle to open the More Complicated Functions Worksheet

Click on the rectangle to open the More Complicated Functions

Model Answers

These resources explain how more complicated functions can be created from five basic functions

More Complicated Functions

https://portal.uea.ac.uk/documents/6207125/8198422/bridging+algebra+calculus+more+complicated+functions.pdf

https://portal.uea.ac.uk/documents/6207125/8198422/bridging+algebra+calculus+more+complicated+functions+worksheet.pdf

https://portal.uea.ac.uk/documents/6207125/8198422/bridging+algebra+calculus+more+complicated+functions+model+answers.pdf

Definition and tips for identifying straight lines. Looking more closely at the gradient, intercepts and common straight lines

What is a Straight Line? Webcast

What is a Straight line?

Click on the rectangle to open the What is a Straight Line?

Study Guide

Resources about sketching different types of straight lines: horizontal, vertical and diagonal. They show two separate methods for sketching a line and discusses the difference between plotting and sketching.

Sketching Straight Lines Webcast

Sketching Straight Lines

Click on the rectangle to open the Sketching Straight Lines Study Guide

A quadratic function is a simple power function (order 2). These resources describe the connection between a general quadratic function and its graph.

Quadratic

Functions

The trigonometric identities (sine, cosine and tangent) are properties of the angles in right-angled triangles. Sine and cosine are basic functions.

Click on the rectangle to open the Trigonometric Ratios

Study Guide

Trigonometric

Ratios Webcast

Click on the rectangle to open the Trigonometric Ratios

Worksheet

Click on the rectangle to open the Trigonometric Ratios

Model Answers

https://portal.uea.ac.uk/documents/6207125/8197337/steps+into+trigonometry+trigonometric+ratios+sine+cosine+and+tangent.pdf

https://portal.uea.ac.uk/documents/6207125/8197337/steps+into+trigonometry+trigonometric+ratios+sine+cosine+and+tangent+worksheet.pdf

https://portal.uea.ac.uk/documents/6207125/8197337/steps+into+trigonometry+trigonometric+ratios+sine+cosine+and+tangent+model+answers.pdf

Trigonometric Ratios: Sine, Cosine and Tangent

Resources describing how to find the equation of a straight line for various given situations in both mathematics and experiments.

Finding Equations of Straight Lines Webcast

Click on the rectangle to open the Finding Equations of Straight Lines

Study Guide

https://portal.uea.ac.uk/documents/6207125/8194890/steps+into+algebra+quadratic+functions.pdf

Click on the rectangle to open the Sketching a Graph

Study Guide

Sketching a Graph

Sketching a Graph

Webcast

https://portal.uea.ac.uk/documents/6207125/8198428/bridging+algebra+calculus+sketching+a+graph.pdf

Definite

Integrals

Definite integrals involve calculating areas and values of integrals. Visualising the problems by sketching the region you are interested in is important.

Definite

Integrals Webcast

Click on the rectangle to open the Definite

Integrals Study Guide

https://portal.uea.ac.uk/documents/6207125/8199682/steps+into+calculus+definite+integrals.pdf

Stationary Points

These resources look at the stationary points (maximums, minimums and points of inflexion) on graphs.

Stationary Points Webcast

Click on the rectangle to open the Stationary Points Study Guide

The exponential function is well-known in science and economics. It is also a basic function. These resources give some basics definitions and graphs.

Exponential

Functions

Exponential Functions Webcast

Click on the rectangle to open the Exponential Functions

Study Guide

These resources explain the language and mathematics surrounding logarithms, specifically the logarithmic transformation. The logarithm function is a basic function.

Basics of Logarithms

Basics of Logarithms Webcast

Click on the rectangle to open the Basics of Logarithms Worksheet

Click on the rectangle to open the Basics of Logarithms Study Guide

The laws of logarithms are the rules which control the manipulation and simplification of logarithms. As logarithms are very common in mathematics, it is well-worth mastering them.

Laws of Logarithms

Laws of Logarithms Webcast

Click on the rectangle to open the Laws of Logarithms Study Guide

Five Basic Functions

Five Basic Functions

Webcast

Click on the rectangle to open the Five Basic Functions Factsheet

A factsheet with the properties of the five basic functions power, sine, cosine, exponential and logarithm.

https://portal.uea.ac.uk/documents/6207125/8221205/bridging+algebra+calculus+five+basic+functions+factsheet.pdf

https://portal.uea.ac.uk/documents/6207125/8198419/bridging+algebra+calculus+using+functions.pdf

https://portal.uea.ac.uk/documents/6207125/8198419/bridging+algebra+calculus+using+functions+worksheet.pdf

https://portal.uea.ac.uk/documents/6207125/8198419/bridging+algebra+calculus+using+functions+model+answers.pdf

https://portal.uea.ac.uk/documents/6207125/8198425/bridging+algebra+calculus+inverse+functions+and+graphs.pdf

Quadratic Functions Webcast

Click on the rectangle to open the Quadratic Functions

Study Guide

https://portal.uea.ac.uk/documents/6207125/8198443/bridging+algebra+calculus+exponential+functions.pdf

https://portal.uea.ac.uk/documents/6207125/8198446/bridging+algebra+calculus+basics+of+logarithms.pdf

https://portal.uea.ac.uk/documents/6207125/8198449/bridging+algebra+calculus+the+laws+of+logarithms.pdf

https://portal.uea.ac.uk/documents/6207125/8203701/other+essential+skills+plotting+a+graph+by+hand.pdf

https://portal.uea.ac.uk/documents/6207125/8198440/bridging+algebra+calculus+simultaneous+equations.pdf

Click on the rectangle to open the Simultaneous Equations Study Guide

Solving and understanding the meaning of simultaneous equations can be very useful. They describe many complicated situations and continue to be relevant in higher mathematics.

Simultaneous Equations

Finding equations of straight lines

Simultaneous Equations Webcast

https://portal.uea.ac.uk/documents/6207125/8198434/bridging+algebra+calculus+finding+equations+of+straight+lines.pdf

https://portal.uea.ac.uk/documents/6207125/8198437/bridging+algebra+calculus+sketching+straight+lines.pdf

Click on the rectangle to open the Sketching Straight Lines Model Answers

Click on the rectangle to open the Sketching Straight Lines Worksheet

https://portal.uea.ac.uk/documents/6207125/8198437/bridging+algebra+calculus+sketching+straight+lines+worksheet.pdf

https://portal.uea.ac.uk/documents/6207125/8198437/bridging+algebra+calculus+sketching+straight+lines+model+answers.pdf

https://portal.uea.ac.uk/documents/6207125/8198431/bridging+algebra+calculus+what+is+a+straight+line+worksheet.pdf

Click on the rectangle to open the What is a Straight Line?

Model Answers

Click on the rectangle to open the What is a Straight Line?

Worksheet

https://portal.uea.ac.uk/documents/6207125/8198431/bridging+algebra+calculus+what+is+a+straight+line+model+answers.pdf

https://portal.uea.ac.uk/documents/6207125/8198431/bridging+algebra+calculus+what+is+a+straight+line.pdf

What is Differentiation? Webcast

https://portal.uea.ac.uk/documents/6207125/8199642/steps+into+calculus+what+is+differentiation.pdf

Resources describing the meaning and language of differentiation. It helps to understand the connection between the gradient of a straight line and the derivative.

What is Differentiation?

Click on the rectangle to find out more about differentiation

Click on the rectangle to open the What is Differentiation? Study Guide

http://prezi.com/7enhnyzgjkov/steps-into-calculus/

Being able to sketch a graph from its equation plays an increasingly important role as mathematics gets more complicated. These resources offer tips to help you do it successfully.

Click on the rectangle for more resources about Trigonometry

http://prezi.com/xx9s9ksxtenl/steps-into-trigonometry/

Click on the rectangle to find out more about integration

https://portal.uea.ac.uk/documents/6207125/8198416/bridging+algebra+calculus+functions.pdf

https://portal.uea.ac.uk/documents/6207125/8198416/bridging+algebra+calculus+functions+worksheet.pdf

https://portal.uea.ac.uk/documents/6207125/8198416/bridging+algebra+calculus+functions+model+answers.pdf

https://portal.uea.ac.uk/documents/6207125/8198446/bridging+algebra+calculus+basics+of+logarithms+worksheet.pdf

http://prezi.com/7enhnyzgjkov/steps-into-calculus/

https://portal.uea.ac.uk/documents/6207125/8199660/steps+into+calculus+stationary+points.pdf

Click on the rectangle to open the Basics of Logarithms Model Answers

https://portal.uea.ac.uk/documents/6207125/8198446/bridging+algebra+calculus+basics+of+logarithms+model+answers.pdf

Click on the rectangle to open the Laws of Logarithms Worksheet

Click on the rectangle to open the Laws of Logarithms Model Answers

https://portal.uea.ac.uk/documents/6207125/8198449/bridging+algebra+calculus+the+laws+of+logarithms+worksheet.pdf

https://portal.uea.ac.uk/documents/6207125/8198449/bridging+algebra+calculus+the+laws+of+logarithms+model+answers.pdf

Click on the rectangle to open the Finding Equations of Straight Lines

Worksheet

https://portal.uea.ac.uk/documents/6207125/8198434/bridging+algebra+calculus+finding+equations+of+straight+lines+worksheet.pdf

Click on the rectangle to open the Simultaneous Equations Worksheet

Click on the rectangle to open the Simultaneous Equations Model Answers

https://portal.uea.ac.uk/documents/6207125/8198440/bridging+algebra+calculus+simultaneous+equations+worksheet.pdf

https://portal.uea.ac.uk/documents/6207125/8198440/bridging+algebra+calculus+simultaneous+equations+model+answers.pdf

Click on the rectangle to open the Finding Equations of Straight Lines

Model Answers

https://portal.uea.ac.uk/documents/6207125/8198434/bridging+algebra+calculus+finding+equations+of+straight+lines+model+answers.pdf