1. Section 5.2 “Relations and Functions” Wednesday, October 27, 2010

2. Warmup Look at the graph on the board: 1.Why does this graph not start at zero? 2.Why is the graph not a straight slanted line? 3.What does the flat part at the top of the graph represent? 4.A plane is flying from New York to London. Sketch a graph of the plane’s altitude – include take off, during the flight, and landing. Label each section!

3. A plane is flying from New York to London. Sketch a graph of the plane’s altitude during the flight. Label each section!

4. _________________________________________________________ Relation – Set of ordered pairs. Domain – All of the x-values (or the first set of numbers) Range – All of the y-values (or the 2 nd set of numbers) Years of Education Median Salary 1019 1326 1430 1535 1741

5. FUNCTION: Vertical Line Test: Relation with EXACTLY one value in the Range for every value in the Domain. SO, you can’t have two numbers in the Domain that are the same! {(1,2), (4, 10), (9, 2), (10, 5)} If a vertical line passes through MORE than one point it is NOT a function. HELPFUL HINT: D is before R…X is before Y…Domain goes with the first set of numbers and Y goes with the 2 nd set of numbers!

6. Ex) Use the Vertical Line Test to determine whether the relation is a function. Relation {(4,-2),(1,2),(0,1),(2,-2)}

7. Mapping Diagrams Ex) { (0,2), (1,3), (2,4) } Domain Range 012012 234234

8. Ex) { (2,8), (-1,5), (0,8), (-1,3), (-2,3) }

9. Ex) Are these functions? Domain Range 0 1 -3 7 10 23472347 568568 Domain Range

10. FUNCTION RULE INPUT (Domain) OUTPUT (Range) X F (x) 3x + 4

11. FUNCTION RULE a. Evaluate ƒ(x) = –5x + 25 for x = –2. b. Evaluate y = 4x 2 + 2 for x = 3.

12. Finding the RANGE Evaluate the function rule ƒ(g) = –2g + 4 to find the range for the domain {–1, 3, 5}.

13. Homework Workbook page 60 (1-23 all)

14. Finding the RANGE in the Graphing Calculator 1.Input the function rule into the Y= Button. 2.In TblSet, start at -1 and count by 1. 3.Then hit 2 nd – TABLE. Use the arrow keys to scroll up and down the table to find the necessary domain/range pairs.