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Functions and Relations. You should be taking notes. Relation: any set of ordered pairs. We use Set Notation to indicate that a group of numbers is part of a given set. . Relation: any set of ordered pairs.

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functions and relations

Functions and Relations

You should be taking notes

slide2

Relation: any set of ordered pairs.

We use Set Notation to indicate that a group of numbers is part of a given set.

slide3

Relation: any set of ordered pairs.

We use Set Notation to indicate that a group of numbers is part of a given set.

Indicate a set by using curly braces.

Example: { (0,1) (1,8) (2,5) (3,7) }

slide5

Input: The first number in the ordered pair. It is the X coordinate.

Example: The ordered pair (5,8) has an input value of 5.

slide7

Output: the second number in an ordered pair. It is the Y coordinate.

Example: The ordered pair (9, 15) has an output value of 15.

slide8

Function: a relation where every input has exactly one output.

Hint: A set where there are repeated X’s, cannot be a function.

A set where there are repeated Y’s CAN be a function.

slide9

Function: a relation where every input has exactly one output.

Hint: A set where there are repeated X’s, cannot be a function.

A set where there are repeated Y’s CAN be a function.

Example:

{ (6,4) (3,9) (3,2) } Cannot be a function.

{ (9,3) (4,3) (2,8) } CAN be a function.

slide11

Another way to think about this is the “Vertical Line” rule.

Remember that when we talk about ordered pairs, we’re talking about points that can be plotted on the Cartesian grid.

slide12

Another way to think about this is the “Vertical Line” rule.

Remember that when we talk about ordered pairs, we’re talking about points that can be plotted on the Cartesian grid.

(That’s this thing) 

slide13

To see what the Vertical line rule is all about, plot the following points on the Cartesian Grid:

(4,2) (-3,2) (2,2) (-2,2)

slide14

To see what the Vertical line rule is all about, plot the following points on the Cartesian Grid:

(4,2) (-3,2) (2,2) (-2,2)

It should look like this 

slide15

To see what the Vertical line rule is all about, plot the following points on the Cartesian Grid:

(4,2) (-3,2) (2,2) (-2,2)

Now draw a line through your points.

slide16

WRITE THIS DOWN!

The Vertical Line Rule: if you can draw a vertical line (up and down) through the line connecting your points without hitting it TWICE, your relation is a function

slide17

The Vertical Line Rule says that if you can draw a vertical line (up and down) through the line connecting your points without hitting it TWICE, your points are a function.

slide18

The Vertical Line Rule says that if you can draw a vertical line (up and down) through the line connecting your points without hitting it TWICE, your points are a function.

So here’s a vertical line on the graph 

slide19

The Vertical Line Rule says that if you can draw a vertical line (up and down) through the line connecting your points without hitting it TWICE, your points are a function.

So here’s a vertical line on the graph 

It can only pass through our line at ONE point, so these points must represent a function!

slide21

Here’s an example of a set that does NOT pass the Vertical Line Test.

Plot the following points:

(2,2) (0,2) (-2,1)

(-2,-1) (0,-2) (2,-2)

slide22

Here’s an example of a set that does NOT pass the Vertical Line Test.

Plot the following points:

(2,2) (0,2) (-2,1)

(-2,-1) (0,-2) (2,-2)

Should look like this 

slide23

Here’s an example of a set that does NOT pass the Vertical Line Test.

Plot the following points:

(2,2) (0,2) (-2,1)

(-2,-1) (0,-2) (2,-2)

Now draw a line connecting them, like this 

slide24

Here’s an example of a set that does NOT pass the Vertical Line Test.

Plot the following points:

(2,2) (0,2) (-2,1)

(-2,-1) (0,-2) (2,-2)

NOW if you draw a vertical line, you’ll see that it will hit the points of the line in more than one spot!

AAHHH! This set is NOT a function!!!!

slide26

Domain: the set of all input values in a function.

So, looking back at the function from earlier, what is the Domain? (4,2) (-3,2) (2,2) (-2,2)

slide27

Domain: the set of all input values in a function.

So, looking back at the function from earlier, what is the Domain? (4,2) (-3,2) (2,2) (-2,2)

Answer: {4, -3, 2, -2}

slide28

Range: the set of all output values in a function.

So, looking back at the function from earlier, what is the Range? (4,2) (-3,2) (2,2) (-2,2)

slide29

Range: the set of all output values in a function.

So, looking back at the function from earlier, what is the Range? (4,2) (-3,2) (2,2) (-2,2)

Answer: {2}

slide30

Any scenario with variables can be a relation and a function. In the following scenarios, write the input, output, and tell whether or not it is a function.

Each student in your class tells his or her birthday. (Hint: think about what the graph would look like)

Each student in your class tells his or her phone number.

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