140909 Notes Algebra Lesson 1.6­ Represent Functions as Rules and Tables.notebook
September 09, 2014
WARM UP­
Perimeter of the given figure is 24 inches and the value of x is 6 inches. What is the value of y?
x
x
2y
y
y
Aug 30­10:11 AM
OPENING QUESTION­
The table shows the fuel efficiency of four compact cars from one manufacturer in model year 2004.
Write a rule for the cars' highway fuel efficiency as a function of their city fuel efficiency.
Another of the manufacturer's cars has a city fuel efficiency of 30 miles per gallon. Predict the highway fuel efficiency.
Sep 2­11:55 AM
1
140909 Notes Algebra Lesson 1.6­ Represent Functions as Rules and Tables.notebook
September 09, 2014
UNIT 1­
LESSON 6: Represent Functions as Rules and Tables
OBJECTIVES:
• Define and use the vocabulary term: relation, function, domain, range, independent variable, dependent variable.
• Identify the set of values that makes up the domain and range of functions.
• Identify a relation as a function.
• Make a table of values for a given function.
• Make a rule for a function given a table of values.
• Write a function rule for a real­world problem.
Nov 2­2:31 PM
CLASS NOTES­
When you pump gas or make any purchases, the cost depends on the amount of gas pumped or items purchased. In this situation, the cost is a function of the number of gallons purchased.
DEFINITION­
A relation pairs inputs and outputs. A function is a relation that pairs a set of input numbers, called the domain, with a set of output numbers, called the range.
A function with pairs inputs with one and only one output.
(input, output)
( x, f(x))
Feb 11­8:55 AM
2
140909 Notes Algebra Lesson 1.6­ Represent Functions as Rules and Tables.notebook
September 09, 2014
CLASS PROBLEM­
Objective: Identify the domain and range of the function.
The table shows the cost of various amounts of unleaded gas from the same pump. Identify the domain and the range of the function.
Feb 22­12:02 PM
CLASS NOTES­
A function can be represented using a mapping diagram. REMEMBER: for a relation to be a function each input can be paired with one and only one output.
Sep 7­1:19 PM
3
140909 Notes Algebra Lesson 1.6­ Represent Functions as Rules and Tables.notebook
September 09, 2014
CLASS PROBLEM­
Objective: Identify a relation as a function.
Decide whether the relation is a function.
Feb 22­12:02 PM
CLASS NOTES­
A function can be represented by using a rule that relates an input variable called the independent variable with an output variable called the dependant variable because its value depends on the input.
Sep 7­1:23 PM
4
140909 Notes Algebra Lesson 1.6­ Represent Functions as Rules and Tables.notebook
September 09, 2014
CLASS PROBLEM­
Objective: Given a function and domain, make a table values.
Make a table of values for the function y = 2x for the domain: 0,2,5,7.
Feb 22­12:02 PM
CLASS PROBLEM­
Objective: Write a function rule given a table of values.
Write a rule for the function described by the table below.
Feb 22­12:02 PM
5
140909 Notes Algebra Lesson 1.6­ Represent Functions as Rules and Tables.notebook
September 09, 2014
CLASS PROBLEM­
Objective: Write a function rule for a real­world situation.
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 tickets you buy. Feb 22­12:02 PM
OPENING QUESTION­Revisited
The table shows the fuel efficiency of four compact cars from one manufacturer in model year 2004.
Write a rule for the cars' highway fuel efficiency as a function of their city fuel efficiency.
Another of the manufacturer's cars has a city fuel efficiency of 30 miles per gallon. Predict the highway fuel efficiency.
Nov 15­5:42 PM
6
140909 Notes Algebra Lesson 1.6­ Represent Functions as Rules and Tables.notebook
September 09, 2014
IN CLOSING...
HOMEWORK ­> 1.6
Feb 11­9:16 AM
7