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Functions and RelationsPowerPoint Presentation

Functions and Relations

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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.

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) }

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

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.

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

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.

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.

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.

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.

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)

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)

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

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.

WRITE THIS DOWN! following points on the Cartesian Grid:

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

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.

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

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!

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)

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

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

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!!!!

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

Domain: Line Test. 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)

Domain: Line Test. 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}

Range: Line Test. 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)

Range: Line Test. 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}

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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