2 1 Relations and Functions Algebra 2 What

2 -1: Relations and Functions Algebra 2

What is a Relation �A set of inputs and outputs �Can be represented in 4 different ways: Ordered Pairs Table of Values Mapping Diagram Input x Output y 1 9 1 -11 4 -2 9 10 Graph

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? Mapping Diagram Ordered Pairs Table of Values Input x Output y 32 53 21 32 19 29 16 25 Graph

Domain and Range of a Relation Domain Range � Set of inputs � x coordinates of ordered pair x y 1 $5. 00 2 � Set of outputs � y coordinates of ordered pair 3 4 5 $10. 00 $15. 00 $20. 00 $25. 00 6 $30. 00 Domain: ________________ Range: _________________

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 FUNCTION Complete Got It? p. 62 #3 1). No 2). Yes NOT A FUNCTION

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

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.

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

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

Types of Function Notation �Euhler’s Function Notation: �Mapping Notation:

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

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: Braking distance at speed x: Stopping distance at speed x: y= x.

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

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. Relate Total Cost per Pizza # of Pizzas Define Write Evaluat e The total cost for 5 pizzas is Delivery Fee

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). No, 3 has two values in the range. 4). Ye each value in the domain has only one value in the s, range.

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