# Writing a Function Rule

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Writing a Function Rule

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

Independent and Dependent
y = 3x – 2 Cost of three pounds of apples Hours worked, amount paid Weight of a book, number of pages The circumference of a circle, the measure of the radius The price of a single pair of shoes, the total price of 4 pairs of shoes Number of hours spent typing a paper, length of paper Time spent studying for a test, score on the test

y = 3x – 2 I = x, D = y Cost of three pounds of apples I = # of apples D = Cost I = Hours worked, D = amount paid D = Weight of a book, I = number of pages D = The circumference of a circle, I = the measure of the radius I = The price of a single pair of shoes, D =the total price of 4 pairs of shoes I = Number of hours spent typing a paper, D = length of paper I = Time spent studying for a test, D = score on the test

Function Notation You use the symbol f(x) in place of y
Function notation allows you to see the input value.

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

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

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?”

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”

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.)

Tables of Values 2 1 1 y = 1x ? 2 ÷ 2 = 1 1 ÷ 1 = 1 y = 1x ? y = x + 2

Try these…

Try these…-answers f(x) = -x f(x) = 3x

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.

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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