How do I sketch accurate graphs for rational functions in a short amount of time? (I.e. A step by step guide of sketching graphs)
Often in Further Pure modules for various exam boards a common question in the exam paper will be to sketch a graph for a rational function. The step by step aproach I used is as follows:
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Change the form (if required) of the function to a form where the denominators of fractions have greater order than numerators. Find points of intersection with the axis and min or max points and labelling them on the graph.
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Find the limits of the function (by looking at denominators) and drawing dotted lines on the graph to represent these limits as linear functions (i.e. lines on the graph)
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See which side of limit the graph will travel along on by testing values in function. Then drawing appropriate short lines so you know where the connect the graph.
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Finally, mark any points where the function intersects the limits and connect the graphs lines together smoothly.
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