1. Graphs
Transformations

2. Identify the graph, each is a quadratic with single x2 y y 25
Starter 1 identify each graph
Identify the graph, each is a quadratic with single x2 y y 25 -8 8 x 5 10 x
-64
Each is a quadratic with single x2 y y
5-10 mins discuss answers with students 18 -7 x -5 2 9 x

3. Identify the graph, each is a quadratic with single x2 y 16 y
Starter 2 identify each graph
Identify the graph, each is a quadratic with single x2 y 16 y -4 4 x 10 x
Each is a quadratic with single x2 y y 31
5-10 mins discuss answers with students 36 6 x -5 -4 x 9

4. C1: Graphs 1a Starter: KUS objectives
BAT know and use the six types of transformations to graphs
Starter:

5. y = f(x) is any function or equation of a graph.
Introduction
y = f(x) is any function or
equation of a graph.
This example is a cubic
function/equation.
y = f(x)
There are six basic types of transformation of a graph
i.e. six ways we can move the graph or change its shape

6. Point (x, y) becomes point (x, y+a)
Transf 1
y = f(x) + a
y = f(x) +a
Point (x, y) becomes point (x, y+a)
y = f(x) + a
This is a ‘shift’ in the y-direction

7. Point (x, y) becomes point (x-a, y)
Transf 2
y = f(x)
y = f(x+a) -a
Point (x, y) becomes point (x-a, y)
y = f(x+a)
This is a ‘shift’ in the x-direction, opposite to the sign of number a

8. Draw a sketch graph of 𝒚= 𝒙−𝟑 𝟐 +𝟐
WB 1
Draw a sketch graph of 𝒚= 𝒙−𝟑 𝟐 +𝟐
Include any intersections and
The minimum point

9. Include the image of points A and B
WB 2 Draw a sketch graph of 𝒇 𝒙+𝟒 −𝟐
Include the image of points A and B
B (4, 0)
A (-2, 8)
𝒇 𝒙

10. Notice what happens at the zeros
Transf 3
y = Af(x)
y = f(x)
Notice what happens at the zeros
y = Af(x)
This is a ‘stretch’ in the y-direction, Scale factor A.
Every answer (y-coordinate) gets multiplied by A

11. Notice what happens at the y-intercept y = f(Ax)
Transf 4
Notice what happens at the y-intercept
y = f(Ax)
y = f(x)
y = f(Ax)
This is a ‘stretch’ in the x-direction, Scale factor 1/A
Every x coordinate gets multiplied by 1/A, y values stay the same

12. Include the image of points A and B
WB 3 Draw a sketch graph of 𝒇 𝟑𝒙
Include the image of points A and B
B (6, 0)
A (-3, 9)
𝒇 𝒙

13. Include the image of points A, B and C
WB 4 Draw a sketch graph of 𝟐𝒇 𝒙
Include the image of points A, B and C
C (4,-2)
A (-5, 7)
𝒇 𝒙
B (0, 3)

14. This is a ‘reflection’ in the axis, mirror line y = 0
Transf 5
y = f(x)
y = -f(x)
y = -f(x)
This is a ‘reflection’ in the axis, mirror line y = 0
Every y coordinate gets multiplied by -1

15. Notice what happens at the y-intercept y = f(-x)
Transf 6
Notice what happens at the y-intercept
y = f(-x)
y = f(x)
y = f(-x)
This is a ‘reflection’ in the y-axis, Every x value gets multiplied by -1,
So y values are swapped around

16. Include the image of points A, B and C
WB 5 Draw a sketch graph of 𝒇 −𝒙
Include the image of points A, B and C
B (3, 5)
A (-4, -2)
𝒇 𝒙
C (9, 0)

17. Describe these transformations
WB 6
Describe these transformations
a) −𝒇 𝒙
b) 𝒇 𝒙 +𝟒
c) 𝒇 𝟐𝒙
d) 𝟑𝒇 𝒙 +𝟏

18. Work out the equations of the transformed graphs
WB if 𝒇 𝒙 =𝟐 𝒙 𝟑
Work out the equations of the transformed graphs
a) −𝒇 𝒙
a) −𝒇 𝒙 = -𝟐 𝒙 𝟑
b) 𝒇 𝒙 +𝟒
b) 𝒇 𝒙 +𝟒= 𝟐 𝒙 𝟑 +𝟒
c) 𝒇 𝟐𝒙
c) 𝒇 𝟐𝒙 = 𝟐 (𝟐𝒙) 𝟑 =𝟏𝟔 𝒙 𝟑
d) 𝟑𝒇 𝒙 +𝟏
d) 𝟑𝒇 𝒙 +𝟏=𝟑 𝟐𝒙 𝟑 +𝟏= 𝟔𝒙 𝟑 +𝟏

19. One thing to improve is –
KUS objectives BAT know and use the six types of transformations to graphs
self-assess
One thing learned is –
One thing to improve is –

20. END