Identifying and Writing Functions

Identifying and Representing Functions

by Dana Cook

​What is a Function?

Definition: ​A function is a special relation where each ____________ has exactly one ____________.

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​Characteristics: If you can draw a vertical line anywhere on a graph so that it hits the graph in ________________________________ then it is NOT a function. Fails the VLT (______________________).

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Multiple Choice

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

What is the definition of function?

• Has inputs and outputs

• Every input has only one output

• Inputs have different outputs every time

• x-values and y-values

Multiple Choice

Which graph does NOT pass the vertical line test?

• Graph 1
• Graph 2
• Graph 3
• Graph 4

​Examples of a Function

​1. {(1,2), (2,2), (3,2), (4,2)}

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​2.  

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​3.                          4.

​Non-Examples of a Function

​1.  {(0,0), (1,1), (1,-1), (2,4), (2,-4)}

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​2.

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​3.                               4.

Multiple Choice

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

Is this graph pictured a function?

• Yes

• No

Multiple Choice

Is this table a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this graph pictured a function?

• Yes

• No

Multiple Choice

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)
• (3,4) (4,-3) (7,4) (3, 8)
• (6,-5) (7, -3) (8, -1) (9, 1)
• (2, -2) (5, 9) (5, -7) (1, 4)

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function

Multiple Select

• It is a Function

• Not a Function

Multiple Select

• It is a Function

• Not a Function

Multiple Select

• It is a Function

• Not a Function

​Domain versus Range

​1. The x-values of a function are called ___________ or ___________.

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​2. The y-values of a function are called __________ or ___________.

Multiple Choice

All of the x values or inputs are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

All of the y values or outputs are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

In the given relation, what domain value corresponds to the range value -2?
{(-1,2), (-2,4), (2,5), (0,-2), (2,0)}

• -2
• 0
• 2
• 4

Multiple Choice

Write the domain for {(-4; 3), (2; 1), (0;3), (-3;-2)}

• xE{-2; 1; 3}

• yE{-2; 1; 3}

• xE{-4; -3; 0; 2}

• yE{-4; -3; 0; 2}

Multiple Choice

What is the range of the table?

• {-4, 0, 1, 3}
• {-2, 0, 2, 3}
• {-4, -2, 0, 1, 2, 3}
• { (0, 0), (2, -4), (3, 3), (-2, 1) }

Multiple Choice

Identify the domain of the following relation:

• -6, 14, 2, 28
• (-6,14), (0,32), (2,38), (4,44)
• -6, 0, 2, 4
• 14, 32, 38, 44

Multiple Choice

The following ordered pairs represent a relation.
{(1,3) , (5,15) , (2,6), (4,12) , (3,9)}
What are the range values from least to greatest!

• {1, 5, 2, 4, 3}
• {3, 15, 6, 12, 9}
• {3}
• {3, 6, 9, 12, 15}

​Summary

​1. To be a function:

• ​ ________________ values NEVER repeat.​

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• ​ For each _____________, there is only one ____________

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• ​ The graph MUST pass the __________________________

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​ where _______________________________________

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2. The x-values are the _____________ or ______________

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​ 3. The y-values are the ___________ or ______________