20: Stretches © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules

Stretches Module C1 AQA Edexcel OCRMEI/OCR Module C2 "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"

Stretches We have seen that graphs can be translated. e.g. The translation of the function by the vector gives the function. The graph becomes We will now look at other transformations.

Stretches e.g.1 Consider the following functions: and For In transforming from to the y- value has been multiplied by 4

Stretches e.g.1 Consider the following functions: and For Similarly, for every value of x, the y -value on is 4 times the y -value on is a stretch of scale factor 4 parallel to the y -axis In transforming from to the y- value has been multiplied by 4

Stretches The graphs of the functions are as follows: is a stretch of by scale factor 4, parallel to the y -axis BUT, you may look at the graph and see the transformation differently.

Stretches has been squashed in the x -direction We say there is a stretch of scale factor parallel to the x -axis.

Stretches is a transformation of given by either a stretch of scale factor 4 parallel to the y -axis or a stretch of scale factor parallel to the x - axis

Stretches It is easier to see the value of the stretch in the y direction. Now, for 2 and for 1 The reason for the size of the 2 nd stretch can be seen more easily if we write as To obtain from we multiply every value of y by 4. The x -value must be halved to give the same value of y.

Stretches It is easier to see the value of the stretch in the y direction. The reason for the size of the 2 nd stretch can be seen more easily if we write as To obtain from we multiply every value of y by 4. The x -value must be halved to give the same value of y. Now, for 2 and for 1

Stretches is a stretch of scale factor 4 parallel to the y -axis or is a stretch of scale factor parallel to the x -axis The transformation of to SUMMARY

Stretches SUMMARY  The function is obtained from by a stretch of scale factor ( s.f. ) k, parallel to the y -axis.  The function is obtained from by a stretch of scale factor ( s.f. ), parallel to the x -axis.

Stretches We always stretch from an axis. Using the same axes, sketch both functions. so it is a stretch of s.f. 3, parallel to the y -axis e.g. 2 Describe the transformation of that gives. Solution: can be written as

Stretches (b) Exercises 1. (a) Describe a transformation of that gives. (b) Sketch the graphs of both functions to illustrate your answer. Solution: (a) A stretch of s.f. 9 parallel to the y -axis. OR A stretch of s.f. parallel to the x -axis. ( The 1 st of these is easier, especially if we have, for example )

Stretches Copy the sketch and, using a new set of axes for each, sketch the following, labelling the axes clearly: 2. The sketch below shows a function. (a)(b) Describe each transformation in words. Exercises

Stretches (b)(a) Solution: Stretch, s.f. parallel to the x -axis Stretch, s.f. parallel to the y -axis

Stretches

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Stretches SUMMARY  The function is obtained from  The function is obtained from by a stretch of scale factor ( s.f. ), parallel to the x -axis. by a stretch of scale factor ( s.f. ) k, parallel to the y -axis.

Stretches is a transformation of given by either a stretch of scale factor 4 parallel to the y -axis or a stretch of scale factor parallel to the x - axis e.g. 1

Stretches We always stretch from an axis. Using the same axes, sketch both functions. so it is a stretch of s.f. 3, parallel to the y -axis e.g. 2 Describe the transformation of that gives. Solution: can be written as