_________ and __________ Unit 4 - Relations and Functions

Unit 4 - Relations and Functions Some Definitions- A _________ between two variables ____ and _____ is a set of __________ pairs An ordered pair consists of an x and y ____________ A relation may be viewed as ordered _______, __________ design, _________, ________, or written in sentences x-values are _______, _______, ___________ variable y-values are __________ __________, __________ variable Unit 4 - Relations and Functions

Example 1: What makes this a relation? What is the domain? What is the range? Unit 4 - Relations and Functions

Example 2 – Is this a relation? 4 –5 9 –1 Input –2 7 Output What is the domain? {4, -5, 0, 9, -1} What is the range? {-2, 7} Unit 4 - Relations and Functions

Is a relation a function? What is a function? According to a textbook, “a function is…a relation in which ________ ________is paired with exactly ______ __________” Unit 4 - Relations and Functions 5 5

Is a relation a function? Focus on the x-coordinates, when given a relation If the set of ordered pairs has __________ x-coordinates, it ______ A function it is _________ a function Y-coordinates have no bearing in determining functions Unit 4 - Relations and Functions

Unit 4 - Relations and Functions Example 3 :00 Is this a relation? Is this a function? Hint: Look only at the x-coordinates Unit 4 - Relations and Functions

Unit 4 - Relations and Functions :40 Example 4 Is this a function? Hint: Look only at the x-coordinates Is this still a relation? Unit 4 - Relations and Functions

Which relation mapping represents a function? :40 Example 5 Which relation mapping represents a function? Choice One Choice Two 3 1 –1 2 2 –1 3 –2 Unit 4 - Relations and Functions

Unit 4 - Relations and Functions Example 6 Which relation mapping represents a function? A. B. Unit 4 - Relations and Functions

Unit 4 - Relations and Functions Example 7 Which situation represents a function? a. The items in a store to their prices on a certain date b. Types of fruits to their colors A fruit, such as an apple, from the domain would be associated with more than one color, such as red and green. The relation from types of fruits to their colors is not a function. There is only one price for each different item on a certain date. The relation from items to price makes it a function. Unit 4 - Relations and Functions

Unit 4 - Relations and Functions Vertical Line Test Vertical Line Test: a relation is a function if a __________ __________drawn through its graph, passes through only _______ __________. AKA: “The Pencil Test” Take a pencil and move it from left to right (–x to x); if it crosses more than one point, it is not a function Unit 4 - Relations and Functions

Would this graph be a function? Vertical Line Test Would this graph be a function? YES Unit 4 - Relations and Functions

Would this graph be a function? Vertical Line Test Would this graph be a function? NO Unit 4 - Relations and Functions

Unit 4 - Relations and Functions Is the following function discrete or continuous? What is the Domain? What is the Range? Unit 4 - Relations and Functions

Unit 4 - Relations and Functions Is the following function discrete or continuous? What is the Domain? What is the Range? Unit 4 - Relations and Functions

Unit 4 - Relations and Functions Is the following function discrete or continuous? What is the Domain? What is the Range? Unit 4 - Relations and Functions

Unit 4 - Relations and Functions Is the following function discrete or continuous? What is the Domain? What is the Range? Unit 4 - Relations and Functions

Unit 4 - Relations and Functions Domain and Range in Real Life The number of shoes in x pairs of shoes can be expressed by the equation y = 2x. What is the independent variable? What is the dependent variable? Unit 4 - Relations and Functions 19

Unit 4 - Relations and Functions Domain and Range in Real Life Mr. Landry is driving to his hometown. It takes four hours to get there. The distance he travels at any time, t, is represented by the function d = 55t (his average speed is 55mph. What is the independent variable? What is the dependent variable? Unit 4 - Relations and Functions 20

Unit 4 - Relations and Functions Domain and Range in Real Life Johnny bought at most 10 tickets to a concert for him and his friends. The cost of each ticket was $12.50. Complete the table below to list the possible domain and range. 1 2 3   12.50 25.00 37.50 What is the independent variable? What is the dependent variable? Unit 4 - Relations and Functions

Unit 4 - Relations and Functions Domain and Range in Real Life Pete’s Pizza Parlor charges $5 for a large pizza with no toppings. They charge an additional $1.50 for each of their 5 specialty toppings (tax is included in the price). Jorge went to pick up his order. They said his total bill was $9.50. Could this be correct? Why or why not? Susan went to pick up her order. They said she owed $10.25. Could this be correct? Why or why not? Unit 4 - Relations and Functions

Unit 4 - Relations and Functions Domain and Range in Real Life Pete’s Pizza Parlor charges $5 for a large pizza with no toppings. They charge an additional $1.50 for each of their 5 specialty toppings (tax is included in the price). What is the independent variable? What is the dependent variable? Unit 4 - Relations and Functions 23

Unit 4 - Relations and Functions Function Notation f(x) means function of x and is read “f of x.” f(x) = 2x + 1 is written in function notation. The notation f(1) means to replace x with 1 resulting in the function value. f(1) = 2x + 1 f(1) = 2(1) + 1 f(1) = 3 Unit 4 - Relations and Functions

Unit 4 - Relations and Functions Function Notation Given g(x) = x2 – 3, find g(-2) . g(-2) = x2 – 3 g(-2) = (-2)2 – 3 g(-2) = 1 Unit 4 - Relations and Functions

1-6 Relations and Functions Function Notation Given f(x) = , the following. a. f(3) f(3) = 2x2 – 3x f(3) = 2(3)2 – 3(3) f(3) = 2(9) - 9 f(3) = 9 12/3/2018 8:14 AM 1-6 Relations and Functions