1. Transformations

2. I. Parent Functions

3. 𝑦=𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

4. 𝑦=𝑥

5. 𝑦= 𝑥 2

6. 𝑓 𝑥 = 1 𝑥

7. 𝑦= 3 𝑥

8. 𝑦= 𝑥 3

9. 𝑓 𝑥 = 𝑥

10. 𝑦= 𝑥

11. 𝑓 𝑥 =log⁡(𝑥)

12. Transformations address how the changes in a function’s equation, result in changes to its graph.

13. II. Vertical Transformations

14. 𝑓 𝑥

15. 𝑓 𝑥 +𝑘
𝑓 𝑥 𝑠ℎ𝑖𝑓𝑡𝑒𝑑 𝑢𝑝 𝑘 𝑢𝑛𝑖𝑡𝑠.

16. 𝑘
𝑓 𝑥 +𝑘

17. 𝑓 𝑥 −𝑘
𝑓 𝑥 𝑠ℎ𝑖𝑓𝑡𝑒𝑑 𝑑𝑜𝑤𝑛 𝑘 𝑢𝑛𝑖𝑡𝑠.

18. 𝑘
𝑓 𝑥 −𝑘

19. 𝑓 𝑥 = 𝑥

20. 𝑓 𝑥 = 𝑥 +3

21. 𝑓 𝑥 = 𝑥 −4
𝑓 𝑥 = 𝑥

22. 𝑓 𝑥 = 𝑥

23. 𝑓 𝑥 = 𝑥 +2
𝑓 𝑥 = 𝑥

24. 𝑓 𝑥 = 𝑥

25. 𝑓 𝑥 = 𝑥 −4
𝑓 𝑥 = 𝑥

26. III. Horizontal Transformations

27. 𝑓 𝑥

28. 𝑓 𝑥+ℎ
𝑓 𝑥 𝑠ℎ𝑖𝑓𝑡𝑒𝑑 𝑙𝑒𝑓𝑡 ℎ 𝑢𝑛𝑖𝑡𝑠.

29. ℎ
𝑓 𝑥+ℎ

30. 𝑓 𝑥−ℎ
𝑓 𝑥 𝑠ℎ𝑖𝑓𝑡𝑒𝑑 𝑟𝑖𝑔ℎ𝑡 ℎ 𝑢𝑛𝑖𝑡𝑠.

31. ℎ
𝑓 𝑥−ℎ

32. 𝑓 𝑥 = 3 𝑥

33. 𝑓 𝑥 = 3 𝑥−3
𝑓 𝑥 = 3 𝑥

34. 𝑓 𝑥 = 1 𝑥

35. 4
𝑓 𝑥 = 1 𝑥+4
𝑓 𝑥 = 1 𝑥

36. IV. Reflection

37. 𝑓 𝑥

38. −𝑓 𝑥
𝑓 𝑥 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑜𝑣𝑒𝑟 𝑡ℎ𝑒 𝑥−𝑎𝑥𝑖𝑠.

39. −𝑓 𝑥
𝑓 𝑥

40. 𝑓 −𝑥
𝑓 𝑥 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑜𝑣𝑒𝑟 𝑡ℎ𝑒 𝑦−𝑎𝑥𝑖𝑠.

41. 𝑓 𝑥

42. 𝑓 𝑥 = 𝑥 2

43. 𝑓 𝑥 = −𝑥 2
𝑓 𝑥 = 𝑥 2

44. 𝑓 𝑥 =log⁡(𝑥)

45. 𝑓 𝑥 =log⁡(−𝑥)
𝑓 𝑥 =log⁡(𝑥)