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1 Cartesian Coordinate Plane First take a look at………….

Cartesian coordinate plane

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Cartesian Coordinate Plane

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  • 1. 1 Cartesian Coordinate Plane First take a look at.

2. 2 A little history 3. Cartesian Plane 4. 4 Now, lets 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: 9. 9 Cartesian plane x-y plane rectangular coordinate system Also called: 10. 10 Now, lets take a closer look 11. 11 Cartesian plane Divides into Quadrants 12. 12 Cartesian plane I 13. 13 Cartesian plane III 14. 14 Cartesian plane III III 15. 15 Cartesian plane III III IV 16. 16 Cartesian plane III III IV 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, lets look at plotting 29. 29 Now, lets 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, lets look at plotting 33. 33 Now, lets 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, lets look at plotting 37. 37 Now, lets 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, lets look at plotting 41. 41 Now, lets 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, lets look at plotting 45. 45 Now, lets 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, lets 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