Algebra I: Strand 1. Foundations of Functions; Topic 2. Independent and Dependentfilename: AlgI_1-2-1.doc

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Task 1.2.2: Definition of Function . -

The American Heritage Dictionary defines function as something closely related toanother thing and dependent upon it for its existence, value or significance. The wordsfunction and depends can be used interchangeably.

Independent - not subject to control by others, self-governing.

Dependent - Relying on or subject to something else for support

Directions: Examples of Function - Write sentences that represent a function.Determine the independent and dependent parts. Include several different words such asdepends, determines, and 'is a function of' in your statements.

1. How much money I make depends on the number of hours I worka. I control the hours I work - independentb. The money depends on the hours - dependent

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Algebra I: Strand 1. Foundations of Functions; Topic 2. Independent and Dependent

Task 3 Part 1Task 1.2.3: Mathematical Definition of Functions

Look at the following scatter plots, list the coordinate points, connect the points from leftto right and decide if the data represents a function based on the definition of a function.Thedefinition of a function is for each input value there is only one output value.

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Algebra 1: Strand 1. Foundations of Functions; Topic 2. Independent and Dependent

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Look at each of the graphs; can you make a generalization about when a graph followsthe definition of a function?

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Algebra 1: Strand 1. Foundations of Functions; Topic 2.1ndependent and Dependent .. 10

Task 3 Part 2

Use each of the following lists of coordinate points; create a mapping, a table of values,and a scatter plot for each group of coordinate points. Explain which groups ofcoordinate points follow the definition of a function..

1. (-1, -2) (3,3) (-3,6) (0, -3) (5, 1)

2. (-4,9) (-2,5) (1, -1) (-2,7) (4, -3)

3. (-3,17) (-1, -1) (1, -1) (2, -7) (-3, -17)

4. (-1, -5) (2, -5) (4, -5) (-5,2) (-3,3)

Task 3 Part 3

Read each of the following situations and determine whether or not it represents afunctional situation. Justify your answer.

1. The student's age in your classroom matched to their shoe size.2. The numbers on a telephone determine the letters on the phone.3. The letters on a telephone determine the numbers on the phone.4. The months, numbered 1 to 12, establish the number of days in the month.5. Any number times 2 plus 5.6. The cost of renting a car if there is a charge of$0.50 per mile.7. Each student in your grade and the number of minutes they talk on the phone per

month.

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Algebra I: Strand 1. Foundations of Functions; Topic 2. Independent and Dependent .. 10

Task 3 Part 2

Use each of the following lists of coordinate points; create a mapping, a table of values,and a scatter plot for each group of coordinate points. Explain which groups ofcoordinate points follow the definition of a function.

1. (-1, -2) (3,3) (-3,6) (0, -3) (5, 1)

2. (-4,9) (-2,5) (1, -1) (-2,7) (4, -3)

3. (-3,17) (-1, -1) (1, -1) (2, -7) (-3, -17)

4. (-1,-5) (2,-5) (4,-5) (-5,2) (-3,3)

Task 3 Part 3

Read each of the following situations and determine whether or not it represents afunctional situation. Justify your answer.

1. The student's age in your classroom matched to their shoe size.2. The numbers on a telephone determine the letters on the phone.3. The letters on a telephone determine the numbers on the phone.4. The months, numbered 1 to 12, establish the number of days in the month.5. Any number times 2 plus 5.6. The cost of renting a car if there is a charge of$0.50 per mile.7. Each student in your grade and the number of minutes they talk on the phone per

month.