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45: The graph of © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules

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"Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages" Module C2

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e.g. Functions of this type, with a > 1, are called growth functions. The reason for the name can be seen from the graph of In this example, a is greater than 1. The function

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Every time x increases by 1, the y value “grows” by doubling. e.g. e.g.

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Every time x increases by 1, the y value “grows” by doubling. e.g. e.g.

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However far left we go, the graph never reaches the x -axis, even though it looks as though it does on a calculator or computer! e.g. Although is very small, it isn’t zero!

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Tip: When sketching exaggerate the gap between the curve and the x -axis. You don’t need to show the values on the x -axis. It’s the shape that’s important and the intercept on the y -axis.

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Sketch the graph of and, on the same axes, sketch the graph of Solution You can omit these Exercise

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As the value of a increases in the graph gets steeper e.g. All the curves pass through since for all values of a.

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a need not be an integer e.g. Also, if a = 1,

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Instead of growing, the function decays e.g. etc. Values of a between 0 and 1 x x

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Exercise Sketch the graph of and, on the same axes, sketch the graph of Solution

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Values of a between 0 and 1 e.g. N.B. It is not possible for a to be less than zero.

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The function is defined for a > 0 and all values of x. SUMMARY For a > 1, the function grows. a is never zero or negative. For,the function decays. All the curves pass through since for all values of a.

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The following slide contains repeats of information on earlier slides, shown without colour, so that it can be printed and photocopied.

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The function is defined for a > 0 and all values of x. SUMMARY For a > 1, the function grows. a is never zero or negative. For,the function decays. All the curves pass through since for all values of a.

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