1. Properties of Functions
Lesson 2.1

2. Vocabulary A function is a rule Another way to say it:
Assigns to each element from one set
Exactly one element from another one
Another way to say it:
A set of ordered pairs where no two ordered pairs have the same first element
Think of it as a machine
Value goes in the top
Machine alters the value
Generates another value out spout 3 9

3. Ways of Expressing a Function
A function can be reperesented by:
A table
A formula A =  r2
A description
A graph x 7 2 9 3 y 8 4 5

4. Evaluating Possible Functions
Which is a function?
{(2,3), (4,7), (9,3)} {(2,3), (4,7), (2,9)} {(2,3), (4,7), (9,2)}
Vertical Line Test

5. Domain and Range Domain Range
All the possible values of the independent variable, the set of first elements
Range
All the possible values of the dependent variable, the set of second elements x 7 2 9 3 y 8 4 5

6. Domain and Range
Domain
Range
The nature of some functions require restrictions on the domain
What must be excluded for these functions?

7. Domain and Range
The nature of a function determines the extent of the range
Numbers excluded
Maximum or minimum possible values

8. Limits on the Range Determine the range of these functions x y 5 1 8 25 1 8 2 11 3 14 4 17

9. Assignment
Lesson 2.1
Page 66
Exercises 1 – 71 EOO