# Real functions and graphs

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Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this free course, real functions and graphs, you will review the various approaches to sketching graphs and learn some more advanced techniques.

After studying this course, you should be able to:

• understand the definition of a real function
• use the notation for intervals of the real line
• recognise and use the graphs of the basic functions described in the audio section
• understand the effect on a graph of translations, scalings, rotations and reflections
• understand how the shape of a graph of a function features properties of the function such as increasing, decreasing, even and odd.
• Duration 20 hours
• Updated Monday 22nd February 2016
• Intermediate level
• Posted under Mathematics

## Study this free course

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# Real functions and graphs

## Introduction

Many problems are best studied by working with real functions, and the properties of real functions are often revealed most clearly by their graphs. Learning to sketch such graphs is therefore a useful skill, even though computer packages can now perform the task. Computers can plot many more points than can be plotted by hand, but simply ‘joining up the dots’ can sometimes give a misleading picture, so an understanding of how such graphs may be obtained remains important. The object of this course is to review the various techniques for sketching graphs that you may have met in your previous studies, and to extend these methods.

This OpenLearn course is an adapted extract from the Open Unviersity course M208: Pure Mathematics [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]

M208_4