1. Please have a go at sketching the core graph shapes we have come across so far in AS and the beginning of A2 on your own

2. Can you check your partners and discuss any differences
Can you check your partners and discuss any differences. If you can’t settle your disagreements ask the others on your table or me

3. If f(x) = sin x sketch the graph of 2f(x) with x axis in radians
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4. If f(x) = cos x sketch the graph of f(3x) with the x axis in degrees
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5. If f(x) = 1/x sketch the graph of f(x)+5
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6. If f(x) = lnx sketch the graph of f(x-4)
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7. If f(x) = (x-3)(x+4) sketch the graph of -f(x)
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8. If f(x) = (x-2)2(x+4) sketch the graph of f(-x)
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9. Transforming Graphs of Functions
As a summary of the rules from AS maths
f(x + a) is a …
f(x) + a is a …
f(ax) is a …
af(x) is a …
-f(x) is a …
f(-x) is a …
Translation of –a units in the x direction
Translation of a units in the y direction
Stretch in the x direction of scale factor 1/a
Stretch in the y direction of scale factor a
Reflection in the x-axis
Reflection in the y-axis 5D

10. Using the big boards, as a table, can you try and sketch y = 4e2x + 3

11. Transforming Graphs of Functions
y = (x – 2)2 + 3
y = (x – 2)2
y = x2
You need to be able to apply multiple transformations to the same curve
Sketch the graph of:
 Build the equation up from y = x2 7
Translation, 2 units right
Translation, 3 units up

12. Transforming Graphs of Functions
y = 2/x + 5
You need to be able to apply multiple transformations to the same curve
Sketch the graph of:
 Build the equation up from y = 1/x
y = 1/x + 5
y = 1/x
2/5
Translation, 5 units left
Stretch in the y direction, scale factor 2 5D

13. Transforming Graphs of Functions
You need to be able to apply multiple transformations to the same curve
Sketch the graph of:
 Build the equation up from y = cosx 2
y = cos2x 1
y = cosx 90
180
270
360 -1 -2
y = cos2x - 1
Stretch in the x direction, scale factor 1/2
Translation 1 unit down 5D

14. Transforming Graphs of Functions
You need to be able to apply multiple transformations to the same curve
Sketch the graph of:
 Build the equation up from y = x - 1
y = 3|x – 1|
y = x - 1 3
y = |x – 1| 1
1/3 1 1
5/3
y = 3|x – 1| - 2 -1
Reflect negative values in the x-axis
Stretch in the y direction, scale factor 3
You will need to do more than one sketch for these – do not do lots on the same diagram!
Translation 2 units down 5D

15. Using the big boards again can you check and correct the graphs you sketched earlier of y = 4e2x + 3 Showing the correct steps to build up the graph

16. Exercise 5D

17. Transforming Graphs of Functions
B(6,8)
B(6,7)
When you are given a sketch of y = f(x), you need to be able to sketch transformations and show the final position of original co-ordinates
To the right is the graph of y = f(x)
Sketch the graph of:
y = 2f(x) – 1
and state the new coordinates of O, A and B…
B(6,4) O
O(0,-1)
A(2,-1)
y = f(x)
A(2,-2)
A(2,-3)
y = 2f(x)
y = 2f(x) - 1
Vertical Stretch, scale factor 2
 y-values double
Vertical translation 1 unit down
 y-values reduced by 1 5E

18. Transforming Graphs of Functions
y = f(x + 2) + 2
B(4,6)
When you are given a sketch of y = f(x), you need to be able to sketch transformations and show the final position of original co-ordinates
To the right is the graph of y = f(x)
Sketch the graph of:
y = f(x + 2) + 2
and state the new coordinates of O, A and B…
B(6,4)
B(4,4)
A(0,1)
O(-2,2)
O(-2,0) O
A(0,-1)
A(2,-1)
y = f(x)
y = f(x + 2)
Horizontal translation 2 units left
 x-values reduced by 2
Vertical translation 2 units up
 y-values increased by 2 5E

19. Transforming Graphs of Functions
y = 1/4f(2x)
When you are given a sketch of y = f(x), you need to be able to sketch transformations and show the final position of original co-ordinates
To the right is the graph of y = f(x)
Sketch the graph of:
y = 1/4f(2x)
and state the new coordinates of O, A and B…
B(3,4)
B(6,4)
B(3,1)
A(1,-0.25) O
A(1,-1)
A(2,-1)
y = f(x)
y = f(2x)
Horizontal stretch, scale factor 1/2
 x-values divided by 2
Vertical stretch, scale factor 1/4
 y-values divided by 4 5E

20. Transforming Graphs of Functions
y = f(x - 1)
When you are given a sketch of y = f(x), you need to be able to sketch transformations and show the final position of original co-ordinates
To the right is the graph of y = f(x)
Sketch the graph of:
y = -f(x - 1)
and state the new coordinates of O, A and B…
B(6,4)
B(7,4)
A(3,1)
O(1,0) O
A(2,-1)
A(3,-1)
y = f(x)
B(7,-4)
y = -f(x - 1)
Horizontal translation 1 unit right
 x-values increase by 1
Reflection in the x-axis
 y-values ‘swap sign’ (times -1) 5E

21. Exercise 5E and Exercise 5F

22. Assignment 3 for 1 week today