1. Parent Function Transformations

2. Linear b moves up or down Parent Function Transformation Function
Translation
(b)
Move down 4 unit
b moves up or down

3. Linear m stretch and compress Transformation Function Stretch (m)
Compression
(m)
Stretch by a factor of 2
Compressed by a factor of
m stretch and compress

4. Linear m reflection Transformation Function reflection (m)
Reflect over the x-axis
m reflection

5. Transformation Function
a ---stretch
---compression
---reflect over x-axis
h ---moves left or right
***opposite***
k ---moves up or down

6. Quadratic h moves left or right Horizontal Translation (h)
Move left 2 units
Move right 4 units
h moves left or right

7. k moves up or down vertical Translation (k) Move down 2 units
Move up 5 units
k moves up or down

8. Quadratic stretch (a) Compression (a) reflection (a)
Reflect over the x-axis
Stretch by a factor of 2
compressed by a factor of

9. Square Root
Move left 5 units
Move right 4 unit
h moves left or right

10. Move up 3 units
Move down 8 units
k moves up or down

11. Stretch by a factor of 2
Reflect over the x-axis
compressed by a factor of

12. Quadratic h moves left or right Parent Function
Transformation Function
Horizontal Translation
(h)
Move left 2 units
Move right 4 units
h moves left or right

13. Quadratic k moves up or down Transformation Function
vertical Translation
(k)
Move down 2 units
Move up 5 units
k moves up or down

14. Quadratic Transformation Function stretch (a) Compression (a)
reflection
(a)
Reflect over the x-axis
Stretch by a factor of 2
compressed by a factor of

15. Square Root h moves left or right Parent Function
Transformation Function
Horizontal Translation
(h)
Move left 5 units
Move right 4 unit
h moves left or right

16. Square Root k moves up or down Transformation Function
vertical Translation
(k)
Move up 3 units
Move down 8 units
k moves up or down

17. Square Root Transformation Function stretch (a) Compression (a) (a)
reflection
Stretch by a factor of 2
Reflect over the x-axis
compressed by a factor of

18. Absolute Value h moves left or right Parent Function
Transformation Function
Horizontal Translation
(h)
Move right 5 units
Move left 2 unit
h moves left or right

19. Absolute Value k moves up or down Transformation Function
vertical Translation
(k)
Move up 2 units
Move down 4 units
k moves up or down

20. Absolute Value Transformation Function stretch (a)
Stretch by a factor of 2
compressed by a factor of
Compression
(a)
Reflect over the x-axis
reflection
(a)

21. Cubic h moves left or right Parent Function Transformation Function
Horizontal Translation
(h)
Move right 4 units
h moves left or right
Move left 2 units

22. Cubic k moves up or down Transformation Function vertical Translation
Move up 5 units
k moves up or down
Move down 3 units

23. Cubic Transformation Function (a) stretch Compression (a) reflection
Stretch by a factor of 4
Reflect over the x-axis
compressed by a factor of

24. Rational h moves left or right Parent Function Transformation Function
Horizontal Translation
(h)
Move right 4 units
h moves left or right
Move left 2 units

25. Rational k moves up or down Transformation Function (k)
vertical Translation
Move down 5 units
k moves up or down
Move up 3 units

26. Rational Transformation Function stretch (a) Compression (a)
compressed by a factor of
Stretch by a factor of 5

27. Rational Transformation Function reflection (a)
Reflect over the x-axis