1. Functions

2. I. Definitions

3. -7 -6 -2 -4 Relation: A set of ordered pairs ( , ) 1 3 ( , ) 9 ( , ) 8
( , ) 1 3
( , ) 9 -7
( , ) 8 5
( , ) -6 -2
( , ) -4

4. -7 -6 -2 -4 Relation: A set of ordered pairs ( , ) 1 3 ( , ) 9 ( , ) 8
( , ) 1 3
( , ) 9 -7
( , ) 8 5
( , ) -6 -2
( , ) -4
Domain:
The set of first terms
of each pair.

5. -7 -6 -2 -4 Relation: A set of ordered pairs ( , ) 1 3 ( , ) 9 ( , ) 8
( , ) 1 3
( , ) 9 -7
( , ) 8 5
( , ) -6 -2
( , ) -4
Range:
The set of second terms
of each pair.

6. Representations of Relations
1, ,−7 8, −9,−7 −4, 0
Ordered Pairs

7. Representations of RelationsX Y 1 3 -7 9 8 5 -6 -2 -4
Table

8. Representations of Relations
Graph

9. Representations of Relations1 3 9 -7 8 5 -6 -2 -4
Mapping

10. Find the domain and range.
𝐷𝑜𝑚𝑎𝑖𝑛: 0 , ∞
𝑅𝑎𝑛𝑔𝑒: 0 , ∞

11. Find the domain and range.
𝐷𝑜𝑚𝑎𝑖𝑛:(−∞, ∞)

12. Find the domain and range.
𝑦=−2
𝐷𝑜𝑚𝑎𝑖𝑛: 0 , ∞
𝑅𝑎𝑛𝑔𝑒: −2 , ∞

13. Find the domain and range.
𝐷𝑜𝑚𝑎𝑖𝑛: −∞ , ∞
𝑅𝑎𝑛𝑔𝑒: −∞ , ∞

14. Find the domain and range.
𝑦=2
𝑦=−3
𝐷𝑜𝑚𝑎𝑖𝑛: −∞ , ∞
𝑅𝑎𝑛𝑔𝑒: −3, 2

15. Now it’s your turn

16. Find the domain and range.B. C. D.

17. Find the domain and range.
𝑥=−4
𝐷𝑜𝑚𝑎𝑖𝑛:−4
𝑅𝑎𝑛𝑔𝑒: −∞ , ∞

18. Find the domain and range.
𝑦=3
𝐷𝑜𝑚𝑎𝑖𝑛: −∞ , ∞
𝑅𝑎𝑛𝑔𝑒:3

19. Find the domain and range.
𝐷𝑜𝑚𝑎𝑖𝑛: −∞,0
∪ 0,∞ OR
𝑥≠0

20. Find the domain and range.
𝐷𝑜𝑚𝑎𝑖𝑛: −∞,0
∪ 0,∞ OR
𝑥≠0
𝑅𝑎𝑛𝑔𝑒: −∞,0
∪ 0,∞ OR
𝑦≠0

21. Find the domain and range.
𝐷𝑜𝑚𝑎𝑖𝑛: 0,∞
𝑅𝑎𝑛𝑔𝑒: −∞,∞

22. II. Functions

23. -6 -5 -7 -2 Functions: A relation with no repeated domain members
( , ) 3
( , ) 4 -6
( , ) 1 9
( , ) -5 -7
( , ) -2 8
Function

24. -4 -5 -9 -8 Functions: A relation with no repeated domain members
( , ) 7 3
( , ) -4
( , ) 7 1
( , ) -5 -9
( , ) -8 1
Not a Function

25. The Vertical Line Test
Function
Not a Function

26. Now it’s your turn

27. Function or Naw?

28. Function or
Naw?

29. Function or
Naw?

30. Function or
Naw?

31. Function or
Naw?

32. Function or
Naw?

33. `
Function or
Naw?

34. III. Evaluating Functions

35. 𝑓 𝑥 =2𝑥+3
Evaluate and simplify 𝑓(−3)

36. 𝑓 𝑥 =2𝑥+3
𝑓 −3 =2⋅ −3 +3
𝑓 −3 =−6+3
𝑓 −3 =−3

37. 𝑔 𝑥 =− 𝑥 3 +3𝑥
Evaluate and simplify 𝑔(−2)

38. 𝑔 𝑥 =− 𝑥 3 +3𝑥
𝑔 −2 =− − −2
𝑔 −2 =− −8 −6

39. 𝑔 −2 =8−6
𝑔 −2 =2
𝑔 −2 =− −8 −6

40. 𝑔 𝑥 =− 𝑥 3 +3𝑥
𝑔 10 =− ⋅10
𝑔 10 =−
𝑔 10 =−970

41. ℎ 𝑥 = −3𝑥+6
Evaluate and simplify ℎ(5)

42. ℎ 𝑥 = −3𝑥+6
ℎ 5 = −3⋅5+6
ℎ 5 = −15+6

43. ℎ 5 = −9
ℎ 5 =9
ℎ 5 = −15+6

44. 𝑦 𝑥 =𝑙𝑜𝑔 𝑥
Evaluate and simplify 𝑦(1000)

45. 𝑦 𝑥 =𝑙𝑜𝑔 𝑥
𝑦 1000 =𝑙𝑜𝑔 1000
𝑦 1000 =3

46. 𝑝 𝑥 = 4 𝑥
Evaluate and simplify 4 8

47. 𝑝 𝑥 = 4 𝑥
𝑝 8 = 4 8
𝑝 8 =65536

48. Now it’s your turn

49. 𝑓 𝑥 =2𝑥+3
𝑓 7 =2⋅7+3
𝑓 7 =14+3
𝑓 7 =17

50. 𝑓 7
𝑔 8
ℎ −4 𝑦
𝑝 −3

51. 𝑓 𝑥 =2𝑥+3
𝑓 7 =2⋅7+3
𝑓 7 =14+3

52. 𝑓 7 =17
𝑓 7 =14+3

53. 𝑔 𝑥 =− 𝑥 3 +3𝑥
𝑔 8 =−
𝑔 8 =−512+24

54. 𝑔 8 =−488
𝑔 8 =−512+24

55. ℎ 𝑥 = −3𝑥+6
ℎ −4 = −3⋅−4+6
ℎ −4 = 12+6

56. ℎ −4 = 18
ℎ −4 = 12+6
ℎ −4 =18

57. ℎ −4 = 18
ℎ −4 = 18
ℎ −4 = 12+6

58. 𝑦 𝑥 =𝑙𝑜𝑔 𝑥
𝑦 =𝑙𝑜𝑔
𝑦 =−4

59. 𝑝 𝑥 = 4 𝑥
𝑝 −3 = 4 −3
𝑝 −3 =

60. IV. Maximums &
Minimums

61. Relative Maximum:
The largest function (y)
value across a finite domain
Relative Minimum:
The smallest function (y)
value across a finite domain

62. Relative Maximum:
Relative Minimum:

63. Relative Maximum:

64. Relative Minimum:

65. V. Odd & Even
Functions

66. The function 𝑓 𝑥 is an 𝐨𝐝𝐝 𝐟𝐮𝐧𝐜𝐭𝐢𝐨𝐧 if:
𝑓 −𝑥 =−𝑓 𝑥

67. The function 𝑓 𝑥 is an 𝐞𝐯𝐞𝐧 𝐟𝐮𝐧𝐜𝐭𝐢𝐨𝐧 if:
𝑓 −𝑥 =𝑓 𝑥