Functions and Relations

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# Functions and Relations - PowerPoint PPT Presentation

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

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) }

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

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

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.

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.

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

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!

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!

Plot the following points:

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

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

Plot the following points:

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

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

Should look like this 

Plot the following points:

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

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

Now draw a line connecting them, like this 

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: 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: 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)

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)

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)