1. SECT. 1.1 – DAY 2

2. WARM UP

3. OBJECTIVES *Identify functions and use function notation. *Find domain and range of functions.

4. RELATIONS A relation is defined as a set of ordered pairs. Many relations have a rule or formula showing the connection between the two components of the ordered pairs. *Most relations we use in trigonometry are functions.

5. THINKING ABOUT FUNCTIONS… The input in the diagram to the right refers to the __ values of the function. The output in the diagram to the right refers to the __ values of the function. Let’s take a look at the function: y = -3x + 5

6. FUNCTIONS A relation is a function if each value of the independent variable leads to exactly one value of the dependent variable. We can write functions as: y = -3x + 5 Or f(x) = -3x + 5 We say f(x) as “f of x”

7. ARE THESE RELATIONS FUNCTIONS? WHY OR WHY NOT?

8. USING FUNCTION NOTATION Let f(x) = -3x 2 + 2x – 4 Find: 1)f(0) 2)f(-3) 3)f(2)

9. VERTICAL LINE TEST If every vertical line intersects the graph of the function in no more than one point, then the graph is a graph of a function.

10. FINDING DOMAIN AND RANGE OF RELATIONS Domain refers to all of the ______ values in a relation. Range refers to all of the ______ values in a relation.

11. EXAMPLE Find the domain and range of the relation. Is it a function?

12. EXAMPLE Find the domain and range of the relation. Is this a function?

13. EXAMPLE Find the domain and range of the relation. Is this a function ?

14. GROUP ACTIVITY Each group is to come up with five relations on a piece of paper. There must be at least one relation that is not a function. There must be two relations drawn as a graph, two relations written in function notation, and one of your choice. You should have two sheets: one sheet with just the problems on there and one sheet with the answer key. The answer key should express whether the relation is a function as well as finding the relations’ domain and range!

15. INDEPENDENT WORK Work on the back of the worksheet that was last night’s homework.

16. HOMEWORK Domain & Range Worksheet #1-8