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TEACHER:
Mr. Landry  ROOM NUMBER: 111
landrg@portlandschools.org

 

TOPIC: REPRESENT LINEAR FUNCTIONS THROUGH
4 METHODS: VERBAL, TABLE, GRAPH AND ALGEBRA

 

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WHAT I WILL ASSUME
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I am going to assume that you have finished the section Graph 2-Variable First Degree Equation . If you are unsure how to plot ordered pairs or evaluate algebraic expressions please go the the column on your right and see the EXTRAS area.

 

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Represent Linear Functions Through 4 Methods:
Table, Graph, Algebra
and Verbal
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Consider the following ordered pair. The first number, 1, is called the "first coordinate" and the second number, 7, is called the second coordinate. 

opair

The following is called a "set of ordered pairs": { (0,5), (1,7), (2,9), (3,11), (4,13), (5,15), (6,17) }.

A set of ordered pairs uses a left curly bracket, { ,  and the right curly bracket, } , to enclose ordered pairs separated by parentheses. This set of ordered pairs is called a "function." Let me explain to you what a function is by defining a function.

FUNCTIONdefinition: a set of ordered pairs where each first coordinate has a unique second coordinate.

 

Function

ex. 1) { (0,5), (1,7), (2,9), (3,11) }

Comment: Each first coordinate has a unique second coordinate.

ex. 3) { (-4,5), (-1,7), (3,7), (5, -12) }

Comment: Each first coordinate has a unique second coordinate.

 
Not A Function
ex. 2) { (0,5), (1,7), (1,9), (3,11) }

Comment: Notice how the first coordinate 1 has two different second coordinates 7 and 9.

ex. 4) { (-4,5), (-1,7), (3,7), (-4,11) }

Comment: Notice how the first coordinate -4 has two different second coordinates 5 and 11.

 

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REAL WORLD EXAMPLES OF A FUNCTION
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Example 1) Tom is leaving Deering High school and walking towards the Quality Shop. Once he has walked 5 feet he starts his stop watch and keeps track of how far he has walked over a 6 second interval. Below are 4 different ways to describe Tom's 6 second walk. These 4 descriptions represent a function since each first coordinate(time in seconds) has a unique second coordinate(position in feet).

  1. A Verbal Description
  2. An Algebra Equation Description
  3. A Graph Description
  4. A Table Description

all

 

Example 2) Mary is scuba diving along the coast of Portland. As she goes deeper and deeper the pressure of the water on Mary's body gets greater and greater. Mary has a device on her diving suit that tells her the water pressure based on her depth under the water. Below are 4 different ways to describe the water pressure on Mary as she dives deeper into the ocean. These 4 descriptions represent a function since each first coordinate(depth in feet) has a unique second coordinate(pressure in pounds per square inch).

  1. A Verbal Description
  2. An Algebra Equation Description
  3. A Table Description
  4. A Graph Description

THE REAL WORLD SITUATION

DIVER

 

VERBAL DESCRIPTION

The water pressure on Mary's body is 15 times Mary's depth divided by 33.

ALGEBRA DESCRIPTION

p = (15d)/33 where p is the pressure in pounds per square inch(psi) and d is the depth of water in feet.

TEACHER COMMENT: What is pounds per square inch? Well, a square inch is a square 1 inch on each side. 10 pounds per square inch means a 10 pound weight placed on 1 square inch; 100 pounds per square inch means to have a 100 pound weight placed on 1 square inch. See picture below.

psi

TABLE DESCRIPTION

d p  = (15d)/33 (d, p)
0 p  = (15(0))/33 = 0/33 = 0 (0, 0)
10 p  = (15(10))/33 = 150/33 = 4. 546 (10, 4.546)
20 p  = (15(20))/33 = 300/33 = 9. 0909 (20, 9.090)
50 p  = (15(50))/33 = 750/33 = 22.727 (50, 22.727)
70 p  = (15(70))/33 = 1050/33 = 31. 818 (70, 31.818)
110 p  = (15(110))/33 = 1650/33 = 50 (110, 50)

GRAPH DESCRIPTION

diver finished

Maximum Sport Diving, i.e. scuba diving, depth is about 130 feet. Physical changes brought on by water pressure(psi) become greater and greater the deeper one dives, and compressed air breathing(air from a scuba tank) can lead to nitrogen narcossis and other problems during deep dives.

 

!!!!!!!!! IMPORTANT !!!!!!!!!

MOST USEFUL REAL WORLD PROBLEMS
ARE FUNCTIONS

 


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PROBLEM SETS
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1) The United States uses the Fahrenheit measuring system for temperature. Outside of the US the Celsius measuring system for temperature is used. Given the following verbal description make an algebra description, graph description and a table description.

Verbal: Temperature Fahrenheit is 32 more degrees than 9/5 temperature Celsius.

TEMPERATURE CONVERTER

Enter a Celsius temperature in the °C field and then press Calculate to get the Fahrenheit temperature.

OR

Enter a Fahrenheit temperature in the °F field and then press Calculate to get the Celsius temperature.


The current numbers below are for freezing in both scales. Press the Reset button to clear any values in both boxes and the boxes will be reset them to freezing in Celsius and Fahrenheit..

°C =     °F =  


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BACK TO ALGEBRA 1 PART 2 CURRICULUM


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EXTRAS
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... MULTIPLICATION AND PARENTHESES

- PRIME FACTORIZATION

... ORDER OF OPERATIONS
PART 1: PART 2 : PART 3

... MONOMIAL,TERMS AND FACTORS

... THE WORLD OF EXPONENTS

... ADDING SIGNED NUMBERS ON A NUMBER LINE

...VARIABLES: 4 PARTS
PART 1 | PART 2 | PART 3 | PART 4

... ABSOLUTE VALUE

... USING DUDE TO ADD INTEGERS

... USING DUDE TO SUBTRACT INTEGERS

... CARTESIAN COORDINATE SYSTEM:
PART 1 : PART 2 : PART 3  : PART 4 : PART 5
more to come

GEOGEBRA EXERCISES: ADDING LIKE TERMS

  1. ADDING LIKE TERMS 1

  2. ADDING LIKE TERMS 2

GEOGEBRA EXERCISES: EVALUATE AN ALGEBRAIC EXPRESSION

  1. EVALUATE  ALGEBRAIC EXPRESSION 1

  2. EVALUATE ALGEBRAIC EXPRESSION 2

  3. EVALUATE ALGEBRAIC EXPRESSION 3

...GEOGEBRA EXERCISE: SLOPE OF A LINE

...GEOGEGRA EXERCISE: BEST FIT LINE

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TI 83/84
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- BASIC GRAPHING - PART 1 : more to come