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CHAPTER 2

CHAPTER 2. SECTION 2-1. PATTERNS AND ITERATIONS. SEQUENCE An arrangement of numbers in a particular order. The numbers are called terms and the pattern is formed by applying a rule. EXAMPLES OF SEQUENCES. 0, 2, 4, 6, ___, ___, ___ 1, 4, 9, 16, ___, ___,___. EXAMPLES OF SEQUENCES.

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CHAPTER 2

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  1. CHAPTER 2

  2. SECTION 2-1

  3. PATTERNS AND ITERATIONS

  4. SEQUENCE An arrangement of numbers in a particular order. The numbers are called terms and the pattern is formed by applying a rule.

  5. EXAMPLES OF SEQUENCES 0, 2, 4, 6, ___, ___, ___ 1, 4, 9, 16, ___, ___,___

  6. EXAMPLES OF SEQUENCES 2, 8, 14, 20, ___, ___, ___ 1, -2, 4, -8, ___, ___,___

  7. EXAMPLES OF SEQUENCES 4, 12, 20, 28, ___, ___, ___ 2, 6, 18, 54, ___, ___,___

  8. SECTION 2-2

  9. THE COORDINATE PLANE, RELATIONS AND FUNCTIONS

  10. COORDINATE PLANEConsists of two perpendicular number lines, dividing the plane into four regions calledquadrants.

  11. X-AXIS - the horizontal number line Y -AXIS - the vertical number line ORIGIN - the point where the x-axis and y-axis cross

  12. ORDERED PAIR - an unique assignment of real numbers to a point in the coordinate plane consisting of one x-coordinate and one y-coordinate (-3, 5), (2,4), (6,0), (0,-3)

  13. RELATION – set of ordered pairs DOMAIN – the set of all possible x-coordinates RANGE – the set of all possible y-coordinates

  14. MAPPING – the relationship between the elements of the domain and range

  15. FUNCTION – set of ordered pairs in which each element of the domain is paired with exactly one element in the range

  16. SECTION 2-3

  17. LINEAR FUNCTIONS

  18. ABSOLUTE VALUE – the distance of any real number, x, from zero on the number line. Absolute value is represented by |x| |6| = 6, |-6| = 6

  19. LINEAR FUNCTIONS equations in two variables that can be written in the form y = ax + b. Thegraph of such equations are straight lines.

  20. CONSTANT FUNCTION special linear function where the domain consists of all real numbers and where the range consists of only one value y= 2, y = -1, y=3, y= -3

  21. SECTION 2-4

  22. SOLVE ONE-STEP EQUATIONS

  23. ADDITION PROPERTY OF EQUALITY For all real numbers a, b, and c, if a = b, then a + c = b + c and c + a = c + b 22 + 18 = 18 + 22

  24. MULTIPLICATION PROPERTY OF EQUALITY For all real numbers a, b, and c, if a = b, then ac = bc and ca = cb 22•18 = 18•22

  25. Solve the equation q + 18 = 32 -18 = -18 q = 14

  26. SECTION 2-5

  27. SOLVE MULTI-STEP EQUATIONS

  28. Isolate the variable by:a. Using the addition propertyb. Using the multiplication property

  29. SOLVE: 4x + 3 = 15

  30. SOLVE: 4(x – 2) = 3

  31. SOLVE: -3(d – 5) = 18

  32. SECTION 2-6

  33. SOLVE LINEAR INEQUALITIES

  34. ADDITION PROPERTY OF INEQUALITY For all real numbers a, b, and c, if a < b, then a + c < b + c if a > b, then a + c > c + b

  35. MULTIPLICATION PROPERTY OF INEQUALITY For real numbers a, b, and positive number c, if a > b thenac > bc and ca > cb or if a <b, then ac < bc and ca < cb

  36. MULTIPLICATION PROPERTY OF INEQUALITY For all real numbers a, b, and when c is negative, if a > b, then ac < bc and ca < cb or if a < b, then ac > bc and ca > cb

  37. EXAMPLE If a = 70, b = 50, and c = 10 then a + c > b + c or 70 + 10 > 50 + 10 80 > 60

  38. EXAMPLE If a = 2, b = 5, and c = -10 then 2 < 5 2(-10) > 5(-10) -20 > -50

  39. REMEMBER When you multiply or divide both sides of an inequality by a negative number REVERSE the sign.

  40. SOLVING INEQUALITIES Example 3x + 10 < 4

  41. SOLVING INEQUALITIES Example 23 ≥ 8 - 5y

  42. Half-Plane– a graph of a solution of a linear inequality in two variables

  43. Boundary – the edge of the half-plane

  44. Open Half-Plane – does not include the boundary as part of the solution

  45. Closed Half-Plane – does include the boundary as part of the solution

  46. GRAPHING INEQUALITIES x + y ≥ 4 (0,4),(4,0)

  47. SECTION 2-7

  48. DATA AND MEASURES OF CENTRAL TENDENCY

  49. POPULATION – entire group or collections of things

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