Functions review

Identifying Functions

Relations

What is a relation?

A relation is anything with input and output values.

What are input and output values?

X-values are inputs and y-values are outputs.

So?

Relations are anything with x and y values.

Functions are a relation with no repeating input values (no repeating x-values)

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Functions

Match

Match the following words to their definitions.

• Relation

• Function

• Inputs

• Outputs

Anything with inputs and outputs

A relation with no repeating inputs

x-values

y-values

• Anything with inputs and outputs

• A relation with no repeating inputs

• x-values

• y-values

​Because there are 2 arrows that come from the 2 in Set A (the input values) that means this has a repeating x-value!

​​Mapping Diagram

Notice how there are 2 of the number 75 in the High School column (the input values) this means this has a repeating x-value!

​​Table

See how 2 different ordered pairs have a 4 in the x spot? This means this has a repeating x-value!

List of ordered pairs

​Why are these not functions?

Lay your pencil flat on the graph and move it from left to right. If the graph touches your pencil more than once at the same time, it is NOT function.

The graph to the right is not a function because it touches the line more than once at a time, and fails the vertical line test.

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The Vertical Line Test

This graph would touch your pencil twice, and fail the vertical line test

​​Not a Function

This graph does not touch your pencil twice at the same time, and passes the vertical line test

Function

This graph would touch your pencil twice, and fail the vertical line test

Not a Function

This graph does not touch your pencil twice at the same time, and passes the vertical line test

Function

Multiple Choice

Determine if the following is a function or not.

• Function

• Not a function

This is a function because each input has only one arrow.

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This is a function!

Multiple Choice

Determine if the following is a function or not.

• Function

• Not a function

This is a function because each input has only one arrow.

​

This is a function!

Multiple Choice

Determine if the following is a function or not.

• Function

• Not a function

This is not a function because 35 has more than one arrow coming from it.

​

This is not a function!

Multiple Choice

Determine if the following is a function or not.

• Function

• Not a function

This is not a function because 3 has more than one arrow coming from it.

​

This is not a function!

Multiple Choice

Determine if the following is a function or not.

• Function

• Not a function

This is a function because 7 and -7 are two different numbers, so it has no repeating x-values.

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This is a function!

Multiple Choice

Determine if the following is a function or not.

• Function

• Not a function

This is not a function because the input 0 repeats.

​

This is not a function!

Multiple Choice

Determine if the following is a function or not.

• Function

• Not a function

This is a function because none of the x-values are repeating.

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This is a function!

Multiple Choice

Determine if the following is a function or not.

• Function

• Not a function

This is not a function because -4 repeats twice.

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This is not a function!

Multiple Choice

Determine if the following is a function or not.

• Function

• Not a Function

Multiple Choice

Determine if the following is a function or not.

• Function

• Not a Function

Multiple Choice

Determine if the following is a function or not.

• Function

• Not a Function

Multiple Choice

Determine if the following is a function or not.

• Function

• Not a Function

Parts of a Graph

Graphs usually go on a coordinate plane. This is made up of four quandrants. Starting in the top right corner, they are numbered 1-4.

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​Coordinate Planes

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

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

Is this mapping a function or not a function? 

• Function
• Not a Function 

Multiple Choice

Is this set of ordered pairs a function and how can you tell?

• Yes its a function because no y values repeat
• No it's not a function because there are negative numbers
• No it isn't a function because an x value repeats but has different y values 
• No it isn't a function because an y value repeats but has different x values

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.
• Yes, because each x-value has only one y-value paired with it.
• No, because the x-value 11 has two y-values pair with it.
• No, because each x-value has only one y-value paired with it.

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

If f(x) = 2x² + 5x - 3, evaluate f(-1).

• f(-1) = -6

• f(-1) = 1

• f(-1) = -10

• f(-1) = -1

Multiple Choice

Evaluate f(33)

• 33
• 11
• 10
• 8

Multiple Choice

What is the value of x when f(x) = 16?

• x = 4 only

• x = 4 and x = 8

• x = 16

• Not on the graph

Multiple Choice

Evaluate f(x)=-2x+13   for f(10)

• -7
• 1
• -8
• 7

Multiple Choice

If f(x)=6x²-4,
what is f(-1)?

• -2
• 13
• 2
• 0

Multiple Choice

What is f(2)?

• -4
• 8
• 0
• 5

Multiple Choice

What is the value of f(0)?

• -2
• 2
• 4
• 0