Transformations of Functions

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

2. Since the ln1 = 0, a good reference point when graphing y = lnx is (1,0) Notice, when graphing y=lnx, the x-intercept is 1

3. Given the following function, If: a > 0, then shift the graph “a” units up, using the reference point (1,0) If: a < 0, then shift the graph “a” units down, using the reference point (1,0)

4. Given the following function, Since a > 0, then shift the graph “3” units up, using the reference point (1,0)

5. Let’s Graph

6. How will the graph look?

7. Let’s Graph

8. How will the graph look?

9. Let’s Graph

10. How will the graph look?

11. Let’s Graph

12. Given the following function, We get the expression (x - b) and equal it to zero x - b = 0 x = b If: b> 0, then shift the graph “b” units to the right, using the reference point (1,0) If: b< 0, then shift the graph “b” units to the left, using the reference point (1,0)

13. Given the following function, x – 1 = 0 x = 1 Since 1> 0, then shift the graph “1” unit right, using the reference point (1,0)

14. Let’s Graph

15. How will the graph look?

16. Let’s Graph

17. How will the graph look?

18. Let’s Graph

19. How will the graph look?

20. Let’s Graph

21. Graphing Recall: Shift “3” units up since 3 > 0 then we use the expression x + 1, and equal it to zero x +1 = 0 x = -1 Since –1 < 0, then we shift “1” unit to the left

22. Let’s Graph

23. How will the graph look?

24. Let’s Graph

25. How will the graph look?

26. Let’s Graph

27. How will the graph look?

28. Let’s Graph

29. Given the following function, For this equation, c determines how wide or thin it 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

30. Given the following function, Since |5| > 0, then the graph is closer to the y-axis

31. Let’s Graph

32. How will the graph look?

33. Let’s Graph

34. How will the graph look?

35. Let’s Graph

36. How will the graph look?

37. Let’s Graph

38. How will the graph look?

39. Let’s Graph

40. Given the following function, Since 4 > 0, shift the graph “4” units up, using the reference point (1,0) x – 1 = 0 x = 1 Since 1> 0, then shift the graph “1” unit to the right, using the reference point (1,0). Since |5| > 0 shift the graph closer to the y-axis.

41. Let’s Graph

42. How will the graph look?

43. Let’s Graph

44. How will the graph look?

45. Let’s Graph

46. How will the graph look?

47. Let’s Graph

48. How will the graph look?

49. Let’s Graph

50. How will the graph look?