Cartesian Coordinate Plane
- 1. 1 Cartesian Coordinate Plane First take a look at………….
- 4. 4 Now, let’s take a look at…
- 5. 5 Cartesian plane Formed by intersecting two real number lines at right angles
- 6. 6 Cartesian plane Horizontal axis is usually called the x-axis
- 7. 7 Cartesian plane Vertical axis is usually called the y-axis
- 8. 8 Cartesian plane x-y plane Also called:
- 10. 10 Now, let’s take a closer look…
- 17. 17 Cartesian plane The intersection of the two axes is called the origin
- 18. 18 Cartesian plane Math Alert The quadrants do not include the axes III III IV
- 19. 19 Cartesian plane Math Alert A point on the x or y axis is not in a quadrant III III IV
- 20. 20 Cartesian plane Each point in the x-y plane is associated with an ordered pair, (x,y) (x,y) (x,y) (x,y) (x,y)
- 21. 21 The x and y of the ordered pair, (x,y), are called its coordinates Cartesian plane (x,y) (x,y) (x,y) (x,y)
- 22. 22 Math Alert There is an infinite amount of points in the Cartesian plane Cartesian plane
- 23. 23 Take note of these graphing basics
- 24. 24 Always start at (0,0)---every point “originates” at the origin Cartesian plane
- 25. 25 In plotting (x,y) ---remember the directions of both the x and y axis Cartesian plane y x
- 26. 26 Cartesian plane (x,---) x-axis goes left and right
- 27. 27 Cartesian plane (---,y) y-axis goes up and down
- 28. 28 Now, let’s look at plotting…
- 29. 29 Now, let’s look at plotting… (2,1)
- 30. 30 Cartesian plane Start at (0,0) ( , ---) Move right 2 (2,1) + (2,1)
- 31. 31 Cartesian plane (---, ) (---, 1) Move up 1 (2,1) + (2,1)
- 32. 32 Now, let’s look at plotting…
- 33. 33 Now, let’s look at plotting… (4, 2)
- 34. 34 Cartesian plane Start at (0,0) ( , ---) Move right 4 + (4, 2) (4, 2)
- 35. 35 Cartesian plane (---, ) (---, -2) Move down 2 (4, 2) - (4, 2)
- 36. 36 Now, let’s look at plotting…
- 37. 37 Now, let’s look at plotting … ( 3,5)
- 38. 38 Cartesian plane Start at (0,0) ( , ---) Move left 3 ( 3,5)- ( 3,5)
- 39. 39 Cartesian plane (---, ) (---, 5) Move up 5 + ( 3,5)( 3,5)
- 40. 40 Now, let’s look at plotting …
- 41. 41 Now, let’s look at plotting … (0,4)
- 42. 42 Cartesian plane Start at (0,0) (none,---) No move right or left (0,4) (0,4)
- 43. 43 Cartesian plane (0, ) (---, 4) Move up 4 + (0,4) (0,4)
- 44. 44 Now, let’s look at plotting …
- 45. 45 Now, let’s look at plotting … ( 5,0)
- 46. 46 Cartesian plane Start at (0,0) ( ,---) Move left 5 ( 5,0) ( 5,0) -
- 47. 47 Cartesian plane ( ---, 0) No move up or down ( 5,0) ( 5,0)
- 48. 48 Now, let’s look at a little plotting practice…
- 49. 49 Cartesian plane Approximate the coordinates of the point--- Or what is the ‘(x,y)’of the point? Directions:
- 50. 50 Cartesian plane Approximate the coordinates of the point Directions: (2,4)
- 51. 51 Cartesian plane Approximate the coordinates of the point Directions:
- 52. 52 Cartesian plane Approximate the coordinates of the point Directions: ( 4, 2)
- 53. 53 Cartesian plane Approximate the coordinates of the point Directions:
- 54. 54 Cartesian plane Approximate the coordinates of the point Directions: (0,3)
- 55. 55 Cartesian plane Approximate the coordinates of the point Directions:
- 56. 56 Cartesian plane Approximate the coordinates of the point Directions: (3, 3)
- 57. 57 Cartesian plane Approximate the coordinates of the point Directions:
- 58. 58 Cartesian plane Approximate the coordinates of the point Directions: ( 1,6)
- 59. 59 Cartesian plane Approximate the coordinates of the point Directions:
- 60. 60 Cartesian plane Approximate the coordinates of the point Directions: ( 5,0)
- 61. 61 Cartesian plane Find the coordinates of the point two units to the left of the y-axis and five units above the x-axis Directions:
- 62. 62 Cartesian plane Find the coordinates of the point two units to the left of the y-axis and five units above the x-axis Directions: ( 2,5)
- 63. 63 Cartesian plane Find the coordinates of the point on the x-axis and three units to the left of the y-axis Directions:
- 64. 64 Cartesian plane Find the coordinates of a point on the x- axis and three units to the left of the y-axis Directions: ( 3,0)
- 65. Hanapin Mo ‘ko
- 66. 66 Lesson 2: Representations of Relations and Functions
- 67. Relations & Functions Relation: a set of ordered pairs Domain: the set of x-coordinates Range: the set of y-coordinates When writing the domain and range, do not repeat values.
- 68. Relations and Functions Given the relation: {(2, -6), (1, 4), (2, 4), (0,0), (1, -6), (3, 0)} State the domain: D: {0,1, 2, 3} State the range: R: {-6, 0, 4}
- 69. Relations and Functions • Relations can be written in several ways: ordered pairs, table, graph, or mapping.
- 70. Table {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)} x y 3 4 7 2 0 -1 -2 2 -5 0 3 3
- 71. Mapping • Create two ovals with the domain on the left and the range on the right. • Elements are not repeated. • Connect elements of the domain with the corresponding elements in the range by drawing an arrow.
- 72. Mapping {(2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)} 2 1 0 3 -6 4 0
- 73. Functions • A function is a relation in which the members of the domain (x-values) DO NOT repeat. • So, for every x-value there is only one y-value that corresponds to it. • y-values can be repeated.
- 74. Do the ordered pairs represent a function? {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)} No, 3 is repeated in the domain. {(4, 1), (5, 2), (8, 2), (9, 8)} Yes, no x-coordinate is repeated.
- 75. Do the maps represent a function? No, -2 and 0 are not mapped to exactly one element in the range Yes, the domain is mapped exactly to one element in the range
- 76. Do the maps represent a function? No, the domain is mapped to more than one element in the range Yes, the domain is mapped exactly to one element in the range