The Open University since 2006
Alternatively you can skip the navigation by pressing 'Enter'.
Old School With The Hairy Bikers: EPISODE 1Thursday, 30th June 2016 01:05 - BBC Two (England only)Can an intergenerational experiment with 12 teenagers and 12 pensioners benefit both groups? Read more: Old School With The Hairy Bikers: EPISODE 1
The Big C & Me: Episode 3Available until Saturday, 30th July 2016 03:10In the final episode of The Big C & Me we follow three people who face life or death with severe or terminal... Read more: The Big C & Me: Episode 3
Old School With The Hairy Bikers: EPISODE 1Available until Saturday, 30th July 2016 02:10
Thinking Allowed 2016: Good neighbours, The connection between sport and domestic abuseAvailable for over a year
All in the Mind - Summer 2016: All in the Mind Awards Ceremony from the Wellcome Collection in LondonAvailable for over a year
Martin Conway: Flashbulb memoryProfessor Martin Conway, Professor of Cognitive Psychology at City University London talks us... Listen now: Martin Conway: Flashbulb memory
Genius of the Modern WorldIn this three-part OU/BBC co-production for BBC Four, Bettany Hughes explores the life and works... Watch now: Genius of the Modern World
Can renewable energy power the world?Renewable energy sources are gaining an increasing share of world energy supplies. In the next... Try: Can renewable energy power the world? now
Organisations and management accountingThis free course, Organisations and management accounting, examines the nature of organisations,... Try: Organisations and management accounting now
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.
Study this free course
Enrol to access the full course, get recognition for the skills you learn, track your progress and on completion gain a statement of participation to demonstrate your learning to others. Make your learning visible!
Real functions and graphs
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
Copyright & revisions
Originally published: Tuesday, 28th June 2011
Last updated on: Monday, 22nd February 2016
- Creative-Commons: The Open University is proud to release this free course under a Creative Commons licence. However, any third-party materials featured within it are used with permission and are not ours to give away. These materials are not subject to the Creative Commons licence. See terms and conditions. Full details can be found in the Acknowledgements and our FAQs section.
- This site has Copy Reuse Tracking enabled - see our FAQs for more information.
If you enjoyed this, why not follow a feed to find out when we have new things like it? Choose an RSS feed from the list below. (Don't know what to do with RSS feeds?)
Remember, you can also make your own, personal feed by combining tags from around OpenLearn.
All our alternative formats are free for you to download, for more information about the different formats we offer please see our FAQs. The most frequently used are Word (for accessibility), PDF (for print) and ePub and Kindle to download to eReaders*.
- Word (645 KB)
- PDF (1.5 MB)
- ePub 3.0 (32.8 MB)
- ePub 2.0 (535 KB)
- Kindle (223 KB)
- RSS (59 KB)
- HTML (32.9 MB)
- SCORM (32.9 MB)
- OUXML Package (8 KB)
- OUXML File (22 KB)
- IMS Common cartridge
*Please note you will need an ePub and Mobi reader for these formats.