1. 2-1: Relations and Functions Algebra 2

2. What is a Relation A set of inputs and outputs Can be represented in 4 different ways: Ordered PairsMapping Diagram Table of ValuesGraphInput x Output y 19 1-11 4-2 910

3. In 2000, the 4 most populous states(in millions), were CA {32}, TX {21}, NY {19} and FL {16}. The numbers of U.S. Representatives were CA {53}, TX {32}, NY {29} and FL {25}. How can you represent a relation for these data in 4 different ways? Ordered Pairs Mapping Diagram Table of ValuesGraph Input x Output y 3253 2132 1929 1625

4. Domain and Range of a Relation DomainRange Set of inputs x coordinates of ordered pair Set of outputs y coordinates of ordered pair Domain: _______________________________ Range: _________________________________

5. Identifying Functions What is a Function? ◦ A relation in which each element of the domain corresponds with one and only one element in the range. Look for duplicates in the Domain Complete Got It? p. 62 #3 1).2).NoYes

6. Components of Functions Independent VariableDependent Variable Solution depends on it. Input Usually the ______ variable in a table first Depends on the first variable for a value. Output Usually the _______ variable in a table second

7. The Vertical Line Test Used with graphs ◦ If the vertical line touches the graph in more than one point, the graph is not a function.

8. Why the Vertical Line Test Works (3, ) 4 -4

9. Homework: Day 1 p. 65 #11, 13-16, 20, 22, 23, 26, 28, 45-51 odd

10. Euhler’s Function Notation: Mapping Notation: Types of Function Notation

11. Notations are used as a short hand Used mainly with sentences (equations) Letter denotes the name of the function Value of the function Dependent variable Output Argument of the function Independent variable Input Euhler’s Notation: Equation Function Rule

12. Ex.1: Here, the three distances (thinking, braking, stopping) are each a function of speed. Rewrite as Function Rules using Euhler’s f(x). Thinking distance at speed x: y= x. Braking distance at speed x: Stopping distance at speed x:

13. Using Function Notation x Input Function Rule Output -4 0 0.2 For, what is the output for the input -4, 0 and 0.2? 14 2 1.4 Complete Got It? p. 63 #5 a). 9b). 1c). -19

14. A pizza costs $14; the flat delivery fee is $1.50. What function rule models the total cost of the number of pizzas delivered? Evaluate for 5 pizzas. RelateDefineWrite Total Cost Cost per Pizza # of Pizzas Delivery Fee The total cost for 5 pizzas is $71.50 Evaluate

15. Complete Got It? p. 64 #6 Let x = # of bottles purchased Let C = Total cost Complete Lesson Check p. 64 # 1-4 1). 2). 3). 4). No, 3 has two values in the range. Yes, each value in the domain has only one value in the range.

16. Homework: Day 2 p. 65 #8-10, 12, 17-19, 25, 29, 30, 32, 39- 43, 44-52 even