Writing a Function Rule

Independent and Dependent Variables Independent Variable –Will change no matter what –The first member of the ordered pair –Domain –x–x Dependent Variable –Changes depend on the independent variable –The second member of the ordered pair –Range –y–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

Independent and Dependent- answers 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.)

Steps to Write a Function 1.Find change in y values 2.Find change in x values 3.If constant for both – divide change in y by change in x 4.This is what you multiply x by 5.Figure out if you need to add or subtract something to get your y 6.Check another x value to make sure you are correct

Tables of Values ÷ 2 = 1 y = 1x ? y = x ÷ 1 = 1 y = 1x ? y = x + 10

Try these…

Try these…-answers f(x) = -x + 20f(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 = 5. 3 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