1. Do Now:  Identify the domain and range of the following relations:

2. KEY POINTS: - DEFINITION OF A FUNCTION AND HOW TO USE IT - HOW TO DETERMINE WHETHER A RELATION IS A FUNCTION OR NOT - IDENTIFY DOMAIN AND RANGE 2.3 Functions

3. Relations  X= independent  Y= dependent  The amount you pay, in $$, for gas depends on the number of gallons you pumped  X= gallons, y= amount you paid, $$

4. 2.3 : Functions  A function is a relation in which, for each distinct value of the first component of ordered pairs, there is exactly one value of the second component  Rewrite the definition of a function 2 more ways in your own words

5. Decide whether a relation is a function  F= { (1, 2), (-2, 4), (3, -1) }  G= { (1,1), (1, 2), (1,3), (2, 3) }  H= { (-4,1), (-2,1), (-2,0) }  In a function, no two ordered pairs can have the same first component (x) and different second components (y)

6. Input-Output machine  Metaphor to help conceptualize that exactly one value of the dependent variable (y) can be paired with each value of the independent variable (x)  Can’t have multiple outputs for same input

7. Domain and Range  Domain: set of all values of the independent variable, x  Range: set of all value of the dependent variable, y  Example: Give the domain and range of the relation. Tell whether the relation defines a function. (4, 100), (6, 200), (7, 200), (-3, 300)

8. Domain and Range from graph

9. Determining functions from graphs  Vertical line test!  If each vertical line intersects a graph in no more than one point, then the graph is a function  (Think: each x-value matches with only 1 y-value)

10. Homework  2.3 #10-38 even, 45- 52  Due Friday 9/4  Last chance 9/11  Reminder: Friday = last chance for full credit on assignments 1.6 and 1.7