Further Mathematics (AS-Level)
Coordinates and Graphs
Question 1 of 1
1. How confident are you that
a. you can sketch a rational function?
What this might look like in the classroom
It is necessary to sketch many graphs, and use a variety of examples to illustrate the five points made above. Here are some examples to use for each point:
will be found to be an odd graph.
will be found to be an even graph.
is neither odd nor even.
(Well worth showing students some which are neither odd nor even, many students assume that all functions have to be either odd or even).
has two vertical asymptotes.
has a horizontal asymptote. (Try solving
3. Graph close to the asymptote
Try this again
and consider behaviour either side of each asymptote.
4. Graph meeting the axes.
5. Small and large values of
has been met already in (2) but can be considered under this heading as well.
Taking this mathematics further
Students would do well to consider more complex equations;
in order to test their skills more fully.
The use of graph plotting software makes this operation easier to introduce but students need to develop strategies for working with complex equations.
Students need to remember that the x-axis is also the line , and the y-axis is the line . This will help them identify which axis to mark their solutions on. They will need to be able to factorise quadratics, and be able to consider just part of a fraction – for example when looking for the values of that make the denominator equal to zero.
Students may also need reminding of the concept of sketching – as being different from plotting points.
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