1. Transformations of Functions
Viviana C. Castellón
East Los Angeles College
MEnTe
Mathematics Enrichment
through Technology

2. Graph

3. Given the following function,
If: a > 0, then shift the graph “a” units up
If:a< 0, then shift the graph “a” units down

4. Given the following function,
Since a > 0, then the graph will be
shift up “5” units

5. Let’s graph

6. Given the following function,
How will the graph look?

7. Let’s graph

8. Given the following function,
Since a < 0, then the graph will be
shift down “3” units

9. Let’s graph

10. Given the following function,
How will the graph look?

11. Let’s graph

12. Given the following function,
For this equation, b is inside the parenthesis.
We get the expression and equal it to zero.
If: b > 0, then shift the graph “b”
units right
If: b < 0, then shift the graph “b”
units left

13. Given the following function,
We get the expression and equal it to zero.
Since b < 0, then shift the graph
“2” units left

14. Let’s graph

15. Let’s graph
How will the
graph look?

16. Let’s graph

17. Let’s graph
How will the
graph look?

18. Let’s graph

19. Let’s graph
How will the
graph look?

20. Let’s graph

21. Recall:
a > 0 then shift up
a < 0 then shift down
Equal the expression to zero
b > 0 then shift to the right
b < 0 then shift to the left

22. Let’s graph
How will the
graph look?

23. Let’s graph

24. Let’s graph
How will the
graph look?

25. Let’s graph

26. Let’s graph
How will the
graph look?

27. Let’s graph

28. Let’s graph
How will the
graph look?

29. Let’s graph

30. Given the following function,
For this equation, c determines how wide or thin the parabola will be.
if: |c|>1, then the graph is closer to the y-axis
if: |c|=1, then the graph remains the same
if: 0<|c|<1, then the graph is further
from the y-axis
if c is a negative number, then the graph
will reflect on the x-axis

31. Let’s graph

32. Given the following function,
Since |c|>1, then the graph is
closer to the y-axis

33. Let’s graph

34. Let’s graph
How will the graph look?

35. Let’s graph

36. Let’s graph
How will the graph look?

37. Let’s graph

38. Recall:
a>0 then shift up
a<0 then shift down
Equal the expression to zero
b>0 then shift to the right
b<0 then shift to the left
if: |c|>1, then closer to the y axis
if: |c|=1, then the graph is the
same
if: 0<|c|<1, then further from
the y axis

39. Let’s graph
How will the
graph look?

40. Let’s graph

41. Let’s graph
How will the
graph look?

42. Let’s graph

43. Let’s graph
How will the
graph look?

44. Let’s graph

45. Let’s graph
How will the
graph look?

46. Let’s graph

47. Congratulations!! You just completed the transformation of