–6
TRANSFORMATIONS OF CURVES 1
4 y
y=x³
3
2
1
–4 –2 2 4
–1
–2
–3
–4
6 y
4 x
6
2
y=x³
–6 –4 –2
2 4 x
6
–2
–4
–6
6 y
4
y=x³
2
2 4 x
6 –6 –4 –2
–2
–4
–6
By working out what transformation has happened to the red curve y
 x 3
match the six blue and purple curves to the equations given below.
Write the equation next to the curve in each case: y
 x
3 
3 y

3 x 3 y
  x
3 y
  x

3

3 y
  x

3

3 y
 x
3 
3

TRANSFORMATIONS OF CURVES 2
Starting from the curve y
 x 3

2 x

3 , describe what transformation has happened to the original curve, by matching the descriptions with the equations below.
1.
Final Equation of curve y
 x 3

2 x

5
Description
A Shift to the left by 3
2. y
  
2 x

3
3. y
 x
3 
2 x

1
B Reflection in the x axis
C Stretch by a scale factor of 2 parallel to the y axis
4. y
  x

3

3 
2
 x

3
D Stretch by a scale factor 2 parallel to the x axis
5. y x 3 2 x

3
E Shift up by 2
6. y
  x

3

3 
2
 x

3
7. y

2 x
3 
4 x

6
F Reflection in the y axis and a shift up by 2
G Stretch by a scale factor of 1
2 parallel to x axis followed by a shift to the left by 3
H Reflection in the y axis 8. y

8 x 3

4 x

3
3
9. y

3
I Shift to the right by 3 followed by a stretch with scale factor 2 parallel to the y axis
10. y
  
2 x

5
J Shift down by 4
11. y

2
 x

3

3 
4
 x

6
K Stretch by a scale factor of 1
2 parallel to x axis
12. y
 
2 x

3

3   x

3
L Shift to the right by 3
Write your answers below:
1 2 3 4 5 6 7 8 9 10 11 12

TRANSFORMATIONS OF CURVES 3
Starting from the quadratic equation y
 x
2 
2 x

1 , work out the final equation of the curve after the following transformations. Simplify your answers.
Description of Transformation Final Equation
1. Reflection in the x axis
2. Reflection in the y axis
3. Shift up by 4
4. Shift down by 6
5. Shift to the left by 1
6. Shift to the right by 2
7. Stretch by scale factor 3 parallel to y axis
8. Stretch by scale factor 2 parallel to x axis
9. Stretch by scale factor 1
3 parallel to x axis
10. Reflection in y axis followed by shift up by 5
11. Shift to left by 4 followed by reflection in x axis
12. Stretch by factor 2 in y direction followed by a shift down by 6 and to the right by 10

TRANSFORMATIONS OF CURVES: SOLUTIONS
Sheet 1
First graph diagram: Blue is y
  x

3

3
and pink is y
  x

3

3
Second graph diagram: Blue is y
 x
3 
3 and pink is y
 x
3 
3
Third graph diagram: Blue is y
  x 3
and pink is y

3 x 3
Sheet 2
1 2 3 4 5 6 7 8 9 10 11 12
E H J A B L C K D F I G
Sheet 3
1. y
  
2 x

1 7. y

3 x
2 
6 x

3
2.
3.
4.
5.
6. y y y y y




 x x x x x
2
2
2
2
2




2
2
2
6 x x x x




1
5
5
9
8.
9.
10.
11.
12. y y

 x
9
4 x
2
2
 

6 x
1

1 y
 x 2

2 x

6 y
  
6 x

9 y

2 x
2 
44 x

236