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Using Function Notation
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Independent and Dependent Variables
Independent Variable Will change no matter what The first member of the ordered pair Domain x Dependent Variable Changes depend on the independent variable The second member of the ordered pair Range y
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Function Notation You use the symbol f(x) in place of y
Function notation allows you to see the input value.
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An Example If f(x) = 2x + 8, find f(-2)
Replace x with –2 on the right and simplify: f(-2) = 2(-2) + 8 f(-2) = f(-2) = 4
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Another Example If g(a) = -3a – 5, find g(-1).
Replace a in the function rule with –1 and simplify. g(-1) = -3(-1) – 5 g(-1) = 3 – 5 g(-1) = -2
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Another Example If f(x) -
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Using a Table of Values You 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?”
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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 differences That quotient will be the number multiplied by “x”
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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.)
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Tables of Values 2 1 1 y = 1x ? 2 ÷ 2 = 1 1 ÷ 1 = 1 y = 1x ? y = x + 2
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Try these…
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Try these…-answers f(x) = -x f(x) = 3x
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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.
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Try these…answers For f(x) = 4x – 9, find f(x) when x = 3 and x = and 11 For g(x) = 1/3x - 10 find g(27) and g(-15) -1 and -15 Identify the independent variable: The cost to wrap an order is $3 plus $1 per item wrapped. Number of items Identify the dependent variable: Tabor charges $25 for each lawn he mows. Amount earned
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