To Be A Function or Not To Be?

To Be A Function or Not To Be?

Goal:

I can determine whether or not a relation is a function

Functions

• When you put an input, you can only get out one output.

Multiple Choice

Which of the following describes a function?

• Has repeating x-values
• Doesn't pass vertical line test
• Each x-value has exactly one corresponding y-value
• Multiple x-values to one y-value

Inputs and Outputs

• Inputs are the x-values and is called the domain

• In notation they are in the parentheses

• Outputs are the y-values and is called the range

• In notation they are outside the parentheses

Multiple Choice

Which of these is NOT the same

• Range
• Input
• Dependent Value
• Y-Value

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

Relations

• (2,6) is an ordered pair that is in a form of (x,y)

• This is a list of ordered pairs

• {(2, 6) (3, 1) (4, 8)}

Multiple Choice

Is this relation a function?

{(0,1), (1, 4), (2, 5), (3, 7)}

• Function

• Not a Function

Multiple Choice

Is the relation a function? 
{(4,5), (4,-7), (4,2), (4,0), (4,9)}

• Yes
• No

Mapping

• Visual grouping of inputs and outputs connected by arrows

• Mapping will leave out duplicate numbers and instead will just show multiple arrows going to or from the number

• The ovals can be labeled multiple ways

• (input, x, domain)

• (output, y , range)

Multiple Choice

Is this a function?

• Yes

• No

• I'm Confused

• May I phone a friend?

Multiple Choice

Is this a function?

• Yes

• No

• Let me ask my dog...

• Why are there letters in math?

Tables

• They can be presented as columns or rows

• In one column will have x-values (inputs, domain)

• The other column will have the y-values (output, domain)

Multiple Choice

Is this table a function or not a function? 

• Function
• Not a Function

Graphs

• Remember only one y-value (output) for every x-value (input)

• Use the vertical line test

Multiple Choice

• Function
• Not a Function

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function

In Review, all of theses are functions

Each x has only one y

In Review, all of these are NOT a function

In each example, an x-value has more than one y-value

Any questions?

Time to practice!

Multiple Choice

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

• D: {1, -3, -4,}
  R: {0, 1, 2, -4}
• D: {-4, 0, 1, 2}
  R:{-4, -3, 1}
• D: {0, 1, 2, 3, 4}
  R:{1, -3, -4}
• D: {0, 1, 2, -4}
  R: {1, -3, -4, 1}

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

• Function
• Not a Function

Multiple Choice

Which of the following statements is true about a function?

• A graph passes the vertical line test
• A mapping has one arrow leaving each x value.
• A table has repeated x's with the same y value
• All of these are true.

Multiple Choice

In order to be a function the following must be true.

• each x value has only one y value

• each y value has only one x value

• each x has only one y & each y has only one x

• each x and y are equal

Multiple Choice

• It is a function because each x has only one y.
• It's not a function because an x has multiple y's.
• It's not a function because a y has multiple x's.
• It is a function because each y has only one x.

Multiple Choice

• It is a function because each x has only one y.
• It's not a function because an x has multiple y's.
• It's not a function because a y has multiple x's.
• It is a function because each y has only one x.

Multiple Choice

• It is a function because no vertical lines hit it twice.
• It's not a function because a vertical line hits it twice.
• It's not a function because no vertical lines hit it twice.
• It is a function because a vertical line hits it twice.

Multiple Choice

Is this mapping a function and how can you tell?

• Yes its a function cause all the numbers have lines
• No it's not a function because there a 5 in both ovals
• No it's not a function because the x value 5 has y values of  2 & 9
• No it's not a function because the y value 5 has x values of  2 & 9

Multiple Choice

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

Does this mapping diagram represent a function?

• No, because there are repeating input values
• Yes, because there are no repeating input values

Multiple Choice

Is this table a function and how can you tell?

• Yes its a function because there are not variables for missing numbers
• No it's not a function because the y value 4 repeated
• No it isn't a function because the x value 2 is repeated
• No it's not a function because the x value 5 has y values of  10 & 12

Multiple Choice

• It is a function because no vertical lines hit it twice.

• It's not a function because a vertical line hits it twice.

• It's not a function because no vertical lines hit it twice.

• It is a function because a vertical line hits it twice.

Multiple Choice

• Function
• Not a Function

Multiple Choice

Is this a function? Explain.

• Yes; it passes the horizontal line test.

• No; it is not a straight line.

• Yes; it passes the vertical line test.

• No; there is a line connecting the dots.

Multiple Choice

Is it a function?

• It IS a function.

• It IS NOT a function

Multiple Choice

• Function

• Not a Function

Multiple Choice

Which graph does NOT pass the vertical line test?

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

Multiple Choice

Does the graph represent a function?

• Yes, because the vertical line test shows there are no repeating input values
• No, because the vertical line test shows there are repeating input values

Multiple Choice

Is it a function?

• It IS a function. One output for every input.

• It IS NOT a function. One output for every input.

• It IS a function. One input for every output.

• It IS NOT a function. One input for every output.

Multiple Choice

Is it a function?

• It IS a function.

• It IS NOT a function

Multiple Choice

Is it a function?

• It IS a function. It passes the vertical line test.

• It IS NOT a function. It does not pass the vertical line test.

• It IS a function. It passes the horizontal line test.

• It IS NOT a function. It does not pass the horizontal line test.

Multiple Choice

Is it a function?

• It IS a function. No x-values repeat.

• It IS NOT a function, none of the y-values repeat.

• It IS a function. The x- value 4 has two y-values.

• It IS NOT a function. The x- value 4 has two y-values.

Multiple Choice

Is it a function?

• It IS a function.

• It IS NOT a function

Multiple Choice

Is it a function?

• It IS a function.

• It IS NOT a function

Multiple Choice

Choose the answer that describes the image.

• Function

• Linear

• Not a function

• Neither a relation nor a function

Multiple Choice

Is it a function?

• It IS a function. Each input has one output.

• It IS NOT a function. Each output is repeated.

• It IS a function. The x- value repeats.

• It IS NOT a function. Each input is repeated

Multiple Choice

Choose the answer that describes the image.

• Function

• Not a function

• Linear

• Neither a relation nor a function

Multiple Choice

A relation where every input in matches with exactly one output is called what?

• Relation

• Linear

• Exponential

• Function