1.6 Represent Functions as Rules & Tables 1.  Function — a pairing where inputs are paired with only one output  Domain — the set of x values, or inputs.

Slides:



Advertisements
Similar presentations
Identify the domain and range of a function EXAMPLE 1 The input-output table shows the cost of various amounts of regular unleaded gas from the same.
Advertisements

Identify the domain and range of a function EXAMPLE 1 The input-output table shows the cost of various amounts of regular unleaded gas from the same pump.
Functions, Domain and Range
EXAMPLE 3 Make a table for a function
1-4: Patterns and Functions
SOLUTION RUNNING The distance d (in miles) that a runner travels is given by the function d = 6t where t is the time (in hours) spent running. The runner.
Substitute 3 for x and 4 for y. Simplify. Write original equation. Check whether each ordered pair is a solution of the equation. SOLUTION Which ordered.
Functions.
RELATIONS AND FUNCTIONS
TODAY IN ALGEBRA 1…  Warm Up: Writing expressions  Learning Goal: 1.6 You will represent functions as rules and as tables  Independent Practice – NO.
1.2 Represent Functions as Rules and Tables
Function: Definition A function is a correspondence from a first set, called the domain, to a second set, called the range, such that each element in the.
Functions. A function is a relation that has exactly one output for each input.
Represent Functions as Graphs
Section 2.1 – Relations and Functions You can use mappings to describe relationships between sets of numbers. A pairing of items from two sets is special.
7.3 Introduction to Relations and Functions
Pg #4-12e, 13-18, 23, 24, 26, 36,
1.8 Represent Functions as graphs
SOLUTION RUNNING The distance d (in miles) that a runner travels is given by the function d = 6t where t is the time (in hours) spent running. The runner.
3.2 Graph Linear Equations You will graph linear equations in a coordinate plane. Essential Question: How do you graph linear equations? You will learn.
Lesson 3.2 Graph Linear Equations Essential Question: How do you graph linear equations in the coordinate plane? Warm-up: Common Core CC.9-12.F.IF.7a.
4.4 Equations as Relations
Chapter 2.2 Functions. Relations and Functions Recall from Section 2.1 how we described one quantity in terms of another. The letter grade you receive.
Do Now:  Identify the domain and range of the following relations:
1.8 Represent Functions as Graphs
Use the sign shown. A gas station charges $.10 less per gallon of gasoline if a customer also gets a car wash. What are the possible amounts (in gallons)
2.3 Introduction to Functions
Tell whether the pairing is a function. Identify a function EXAMPLE 2 a. a. The pairing is not a function because the input 0 is paired with both 2 and.
Functions. What is a function? A function consists of: A function consists of: A set called the domain containing numbers called inputs, and a set called.
1.2 Represent Functions as Rules and Tables EQ: How do I represent functions as rules and tables??
Do Now 5/19/10 Take out HW from last Thursday.
EXAMPLE 1 Graph a function
Activity 1.2. Some definitions… Independent variable is another name for the input variable of a function Independent variable is another name for the.
Function Sense Unit 2 Phone a friend What is a Function.
Warm-Up Exercises 1. Graph y = –x – 2 with domain –2, –1, 0, 1, and 2. ANSWER.
SOLUTION EXAMPLE 1 Represent relations Consider the relation given by the ordered pair (–2, –3), (–1, 1), (1, 3), (2, –2), and (3, 1). a. Identify the.
Vocabulary Dependent Variable Independent Variable Input Output Function Linear Function.
FUNCTIONS FUNCTIONS DOMAIN: THE INPUT VALUES FOR A RELATION. USUALLY X INDEPENDENT VARIABLE RANGE: THE OUTPUT VALUES FOR A RELATION. USUALLY.
Write a function rule for a graph EXAMPLE 3 Write a rule for the function represented by the graph. Identify the domain and the range of the function.
5.2 Relations and Functions. Identifying Relations and Functions Relation: A set of ordered pairs. You can list the set of ordered pairs in a relation.
Goal: Identify and graph functions..  Relation: mapping or pairing, of input values with output values.  Domain: Set of input values.  Range: set of.
Identify the domain and range of a function EXAMPLE 1 The input-output table shows the cost of various amounts of regular unleaded gas from the same pump.
1.7 Represent Functions as Rules and Tables Essential Question: How do you represent functions as rules and tables? Warm-up: 1. Write an expression:
Warm up X = -1 Why is there only one answer? An absolute value will NEVER be negative.
1.7 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Represent Functions as Graphs.
2.1 Relations and Functions A relation is a set of pairs of input and output values. – There are four different ways to represent relations.
Algebra 1 Section 3.1 Identify and express functions in various forms Many times two quantities are related to each other. The cost of buying gasoline.
1.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Represent Functions as Rules and Tables.
Warm-Up Exercises Warm-up: Countdown to Mastery Week #4 Homework- Page 44 #3-9 all #14-21 all.
Warm-Up Exercises Identify the domain and range of a function EXAMPLE 1 The input-output table shows the cost of various amounts of regular unleaded gas.
Algebra 2 June 18, 2016 Goals:   Identify functions in coordinate, table, or graph form   Determine domain and range of given functions.
Chapter 2 Linear Equations and Functions. Sect. 2.1 Functions and their Graphs Relation – a mapping or pairing of input values with output values domain.
Relations A __________ is a set of pairs of input and out put values.
Input/Output tables.
Function- A pairing of inputs with outputs such that each input is paired with exactly one output. (the inputs can’t repeat) Domain- inputs or x values.
Distinguish between independent and dependent variables.
EXAMPLE 1 Represent relations
Lesson 1.6 Represent Functions as Rules and Tables
Notes Over 2.1 Function {- 3, - 1, 1, 2 } { 0, 2, 5 }
MS Algebra A-F-IF-1 – Ch. 5.1 Functions as Ordered Pairs
Lesson 8.1 Relations and Functions
The domain is the set of inputs: 10, 12, 13,
1.6 Represent Functions as Rules and Tables
VOCABULARY! EXAMPLES! Relation: Domain: Range: Function:
Function Rules and Tables.
Functions Rules and Tables.
Objective SWBAT use graphs to represent relations and functions.
1. Make a table for y = 2x + 3 with domain 0, 3, 6, and 9.
4.3 Writing Functions Objectives
Distinguish between independent and dependent variables.
Presentation transcript:

1.6 Represent Functions as Rules & Tables 1

 Function — a pairing where inputs are paired with only one output  Domain — the set of x values, or inputs  Range — the set of y values, or outputs  Independent Variable — x, or the input  Dependent Variable — y, or the output 2

EXAMPLE 1: Identify the domain and range of a function The input-output table shows the cost of various amounts of regular unleaded gas from the same pump. Identify the domain and range of the function. ANSWER Domain ( the set of inputs): 10, 12, 13, 17 Range (the set of outputs): 19.99, 23.99, 25.99, Input gallons Output dollars

SOLUTION GUIDED PRACTICE 1. Identify the domain and range of the function. Input 0124 Output 5221 Domain ( the set of inputs): 0, 1, 2, and 4 Range (the set of outputs): 1, 2, and 5 4

Tell whether the pairing is a function. a. a. The pairing is not a function because the input 0 is paired with both 2 and 3. EXAMPLE 2: Identify a function 5

b.b. Output Input The pairing is a function because each input is paired with exactly one output. EXAMPLE 2: Identify a function 6

SOLUTION GUIDED PRACTICE Tell whether the pairing is a function Output Input The pairing is a function because each input is paired with exactly one output. 7

SOLUTION GUIDED PRACTICE Tell whether the pairing is a function Output 7422 Input 2. The pairing is not a function because each input is not paired with exactly one output

The range of the function is 0, 4, 10, 14, and 16. x y = 2x 2 2 = = = = = 0 SOLUTION EXAMPLE 3: Make a Table for a Function 9 The domain of the function y = 2x is 0, 2, 5, 7, and 8. Make a table for the function then identify the range of the function.

Write a rule for the function. Input Output SOLUTION x: the input or independent variable y: the output or dependent variable Each output is 2 more than the corresponding input So, the rule for the function is y = x + 2 EXAMPLE 4: Write a Function Rule 10

Concert Tickets You are buying concert tickets that cost $15 each. You can buy up to 6 tickets. Write the amount (in dollars) you spend as a function of the number of tickets you buy. Identify the independent and dependent variables. Then identify the domain and the range of the function. EXAMPLE 5: Write a function rule for a real-world situation 11

SOLUTION Independent variable: n Dependent variable: A Write a verbal model. Then write a function rule. Let n represent the number of tickets purchased and A represent the amount spent (in dollars). Amount spent (dollars) Cost per ticket (dollars/ticket) Tickets purchased (tickets) = EXAMPLE 5: Write a function rule for a real-world situation 12 Function rule: A = 15n

Because you can buy up to 6 tickets, the domain of the function is 0, 1, 2, 3, 4, 5, and 6. Make a table to identify the range. Amount (dollars), A Number of tickets, n The range of the function is 0, 15, 30, 45, 60, 75, and 90. EXAMPLE 5: Write a function rule for a real-world situation 13

SOLUTION GUIDED PRACTICE 1. Make a table for the function y = x - 5 with domain 10, 12, 15, 18, and 29. Then identify the range of the function. x y = x – 5 =512 – 5 =715 – 5 =1018 – 5 =1318 – 29 =24 The range of the function is 5,7,10,13 and

GUIDED PRACTICE 2. Write a rule for the function. Identify the domain and the range. SOLUTION x: the input or independent variable y: the output or dependent variable Each output is 8 times more than the corresponding input So, the rule for the function is y = 8x Domain: 1, 2, 3, 4 Range: 8, 16, 24, 32 Pay (dollars) Time (hours) 15