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

2. Module C1 Module C2 Edexcel AQA OCR MEI/OCR
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3. 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.

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

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

6. BUT, you may look at the graph and see the transformation differently.
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.

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

8. 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

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

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

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

12. 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.

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

14. 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 1st of these is easier, especially if we have, for example )
(b)

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

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

18. The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied.
For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

19. SUMMARY
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.

20. 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

21. 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