MATH 8 4Q

• Relation


  A set of ordered pairs (x, y)
• Function


  A relation in which each x in the domain is paired with one and only one y in the range
• Independent variable


  The variable x whose value determines the value of the dependent variable y
• Dependent variable


  The variable y whose value depends on the value of the independent variable x
• Domain


  The set of all values of the independent variable x
• Range

  The set of all values of the dependent variable y
• Types of relations


  • One-to-one
  • Many-to-one
  • One-to-many
  • Many-to-many
• If a mapping diagram of a relation is one-to-one or many-to-one, then the relation is also called a function
• Examples of relations classified as functions or not


  • {(-4,2), (-2,-3), (3,-1), (6,0), (8,-3)} is a function
  • {(-2, 1), (0, 2), (0, -2), (7,3)} is not a function
  • {(7, 4), (1, 6), (-3, 8)} is not a function
  • {(x, 2x+1)} is a function
• Rule of a function


  The expression that describes the relationship between the independent variable x and the dependent variable y in all the ordered pairs (x, y) of the function
• Calculating distance


  Distance = rate x time, or d = rt, where d is the distance, r is the rate, and t is time
• Area of a rectangle


  Area = length x width, or A=lxw, where A is area, l is length, and w is the width of the rectangle
• Nita's garden dimensions


  • Width = 2 meters
  • Length l = w
  • Length l = 3w
  • Length l = w+2
• Circumference of a circle


  The independent variable is the variable representing the circle, the dependent variable is the circumference
• Sales function


  The function expresses the amount of sales A in terms of the number of T-shirts sold p. The independent variable is p, the dependent variable is A.
• A relation is a set of ordered pairs (x, y). The set of values of x is called the domain and the set of values of y is called the range.
• A relation may be presented using an equation or a mapping diagram. A mapping diagram may be one-to-one, many-to-one, one-to-many, or many-to-many.
• A function is a relation in which each x in the domain is paired one-to-one and many-to-one with one and only one y in the range.
• The set that describes a function is called the rule of the function. This rule describes the relationship between x and y in all the ordered pairs (x, y) of the function.
• Mapping diagrams


  • One-to-one
  • Many-to-one
  • One-to-many
  • Many-to-many
• The given relation {((-3,6), (-1,2), (0, 0), (2, 4), (5, 10)} is a many-to-many mapping diagram
• The given relation {(1,-2), (1, 0), (1, 5), (1, 4), (1, 10)} is a many-to-one mapping diagram
• The given relation {(-10, 7), (-8,7),(1,7), (5,7),(12,7)} is a one-to-many mapping diagram
• The given relation {(2,3), (-2,4), (4, 3), (5, 4). (6.4)} is a many-to-one mapping diagram
• The given relation {(x, y) where y=x=10, 20, 30, 40, 50} is a function
• The given relation {(0, 4), (1, 5), (2,6), (3,7)} has a domain of {0, 1, 2, 3} and a range of {4, 5, 6, 7}
• The function rule for the relation {(0, 4), (1, 5), (2,6), (3,7)} is y=x+4
• The function rule for the relation {((-2,-6). (0,0), (4, 12), (7, 21)} is y=3x
• The function rule for the relation {(-9, 3), (−6, 2), (0, 0), (3, −1)} is y=-x+3
• The function rule for the relation {(20,10), (10, 5), (4, 2), (1,2)} is y=0.5x
• The function rule for the relation {(5,-1), (4,-2), (1, −5), (−1, −7)} is y=-2x-3
• The function rule for the relation {(25, 5), (16, 4), (4, 2), (1, 1)} is y=0.2x
• The function rule for the relation {(−1, 3), (0, 1), (1, −1), (2, −3)} is y=-2x+1
• Perimeter of a rectangle

  The function is P=2l+2w, where P is the perimeter, l is the length, and w is the width. The independent variable is the length l, the dependent variable is the perimeter P.
• Total amount of cookies

  The function is A=nC, where A is the total amount, n is the number of cookies, and C is the cost per cookie. The independent variable is the number of cookies n, the dependent variable is the total amount A.
• Volume of a rectangular prism

  The function is V=Bh, where V is the volume, B is the area of the base, and h is the height. The independent variable is the height h, the dependent variable is the volume V.
• Area of a square

  The function is A=s^2, where A is the area and s is the length of the side. The independent variable is the side length s, the dependent variable is the area A.
• Distance traveled by a tricycle

  The function is d=rt, where d is the distance, r is the average speed, and t is the time. The independent variable is the time t, the dependent variable is the distance d.
• The ordered pairs representing the seats of the students are: (1,1) for Marie, (1,2) for Carlos, (2,2) for Vangie, and (3,5) for Lisa
• The set of all the seats in the plan is a function