1. Writing a Function Rule

2. 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

3. 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

4. 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

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) + 8
f(-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) – 5
g(-1) = 3 – 5
g(-1) = -2

8. 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?”

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 differences
That 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

12. Try these…

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

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…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