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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.
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.
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