2 Independent and Dependent Variables Independent VariableWill change no matter whatThe first member of the ordered pairDomainxDependent VariableChanges depend on the independent variableThe second member of the ordered pairRangey
3 Independent and Dependent y = 3x – 2Cost of three pounds of applesHours worked, amount paidWeight of a book, number of pagesThe circumference of a circle, the measure of the radiusThe price of a single pair of shoes, the total price of 4 pairs of shoesNumber of hours spent typing a paper, length of paperTime spent studying for a test, score on the test
4 Independent and Dependent-answers y = 3x – 2 I = x, D = yCost of three pounds of apples I = # of apples D = CostI = Hours worked, D = amount paidD = Weight of a book, I = number of pagesD = The circumference of a circle, I = the measure of the radiusI = The price of a single pair of shoes, D =the total price of 4 pairs of shoesI = Number of hours spent typing a paper, D = length of paperI = Time spent studying for a test, D = score on the test
5 Function Notation You use the symbol f(x) in place of y Function notation allows you to see the input value.
6 An Example If f(x) = 2x + 8, find f(-2) Replace x with –2 on the right and simplify:f(-2) = 2(-2) + 8f(-2) =f(-2) = 4
7 Another Example If g(a) = -3a – 5, find g(-1). Replace a in the function rule with –1 and simplify.g(-1) = -3(-1) – 5g(-1) = 3 – 5g(-1) = -2
8 Using a Table of ValuesYou can write a rule for a function by analyzing a table of values.Ask yourself “What did I do to the x-values to get the y-values?”
9 Another Way From a table Find the differences between the values in the x column (independent variable)Find the differences in the values in the y coulmn (dependent variable)If there is a constant difference in each, divide the y differences by the x differencesThat quotient will be the number multiplied by “x”
10 Another Way From a table So you have y = x. What else do you have to do to that to get the number in the y column? (Usually add or subtract something.)
11 Tables of Values 2 1 1 y = 1x ? 2 ÷ 2 = 1 1 ÷ 1 = 1 y = 1x ? y = x + 2
14 Try these… For f(x) = 4x – 9, find f(x) when x = 3 and x = 5. For g(x) = 1/3x - 10 find g(27) and g(-15)Identify the independent variable: The cost to wrap an order is $3 plus $1 per item wrapped.Identify the dependent variable: Tabor charges $25 for each lawn he mows.
15 Try these…answersFor f(x) = 4x – 9, find f(x) when x = 3 and x = and 11For g(x) = 1/3x - 10 find g(27) and g(-15)-1 and -15Identify the independent variable: The cost to wrap an order is $3 plus $1 per item wrapped. Number of itemsIdentify the dependent variable: Tabor charges $25 for each lawn he mows. Amount earned