1. 2-4 functions
Objective: define relations, functions, domain and range; evaluate functions; analyze graphs.
Miss battaglia – algebra 1 cp

2. Warm up
Kathy has a computer printer that can print in black, red, blue, or yellow. She has paper in white, tan, and lavender. How many different ways can she print a title page on her color printer?

3. Function Machine

4. Independent/ dependent
Suppose your summer job pays $8.50 an hour. Your pay depends on the number of hours you work. Independent variable - # of hours Dependent variable – pay Pay is a function of the number of hours you work.

5. example
Identify the independent and dependent variable for each situation.
Number of magazines sold and the profit made selling magazines.
Amount of money in the yearbook committee treasury and the number of days the committee can afford to rent camera equipment.

6. definitions Any set of ordered pairs is called a relation.
Write the data in the table as a set of ordered pairs.
Hours Worked
Pay $0 1
$8.50 2
$17.00 3
$25.50
Any set of ordered pairs is called a relation.
A function is a relation that assigns exactly one value of the dependent variable to each value of the independent variable.

7. example
Functions Not functions

8. Determine if each relation is a function.x y 11 -2 12 -1 13 20 7 x y -2 -1 -3 6 3 1

9. Try it on your own
Create a data table that is a relation but not a function. Create a data table that is a function.

10. Quick review!!!

11. y = 3x + 4 Evaluating functions
A function rule is an equation that describes a function.
y = 3x + 4
The rule shows you that y is a function of x.
output values dependent variable
input values independent variables

12. Evaluate the function rule y = 2x2 – 7 for x = - 4.
Example
Evaluate the function rule y = 2x2 – 7 for x = - 4.

13. Evaluate the function rule y= ½x2 for x = 6.
Example
Evaluate the function rule y= ½x2 for x = 6.

14. definitions
The domain of a function is the set of all possible input values. The range of a function is the set of all possible output values.

15. Names of values in a function
independent variable
dependent variable
input
output
domain
range
x – values
y – values

16. bicycling
The distance a wheel moves forward is a function of the number of rotations. The function rule d = 7n describes the relationship between the distance d the wheel in the photo moves in feet and the number of rotations n. Find the range when the domain is {0, 2.5, 8}.

17. Vertical line test
The vertical line test is used to tell if a relation is a function. If the graph passes through the graph more than once, the graph is not a function.

18. Homework
Pg #2, 4, 6, 7, 9, 11, 15, 17, 18, 20, 22, 25, 27