Real functions and graphs

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# 2 Real functions

In Section 1 we formally define real functions and describe how they may arise when we try to solve equations. We remind you of some basic real functions and their graphs, and describe how some of the properties of these functions are featured in their graphs.

Click the link below to open Section 1 (12 pages, 1.8MB).

Section 1 [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]

This PDF contains an audio section in which we revise the properties of some familiar graphs, and introduce some concepts which form the basis of the graph-sketching strategy given in Section 2. Please listen to the audio clips below when you are instructed to do so. Do not worry if you do not fully understand all the details at this stage, but concentrate on the main ideas.

Click play to listen to the audio clip for frames 1 to 4 (6 minutes).

Frames 1-4
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Click play to listen to the audio clip for frames 5 to 9 (7 minutes).

Frames 5-9
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Click play to listen to the audio clip for frames 10 to 13 (7 minutes).

Frames 10-13
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Click play to listen to the audio clip for frames 14 to 17 (7 minutes).

Frames 14-17
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Click play to listen to the audio clip for frames 18 to 21 (3 minutes).

Frames 18-21
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Click play to listen to the audio clip for frames 22 to 25 (5 minutes).

Frames 22-25
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