Representing Relations

Representing Relations

​Domain & Range

​Take Good Notes on this!

​Write down any questions you have.

1. ​Call me over in class to ask about them

2. ​Be ready to ask your questions to me when class starts tomorrow

3. ​We will be practicing this skill tomorrow in class

   1. ​So be ready with your notes

​​Continuous Relations: ​An infinite number of points (ordered pairs). and can be graphed as a smooth line or curve.

​NOTE: A Continuous Relation is represented by an equation and NOT a list of individual ordered pairs.​

​Domain & Range: Continuous Relations

​Domain: All Real Numbers or it will be written as an equation or inequality

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​Range: All Real Numbers or it will be written as an equation or inequality

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​Be sure to take notes on how to properly list domain and range!

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​Inequality Review

​Less Than <

​Less Than or Equal To <

​Meaning you are getting smaller

​

​Greater Than >

​Greater Than or Equal To >

​Meaning you are getting bigger

Domain and Range

• Domain (left to right)

• Range (bottom to top)

Domain (from left to right)

​Range (from bottom to top)

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​​Range Pictured:  

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​Looking from the bottom to the top.

​On the bottom we start at a closed circle at y=-3, then we go up until we stop at an open circle at y=1.

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​(So we are on -3 and we go up until we get to 1)

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Arrows mean infinity

Domain Pictured: All Real Numbers

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​Meaning if we look from the left to the right we are covering all x's possible. The graph has arrows that show it open outward forever which means it will go left and right forever.

Arrows mean infinity

Reminder: When there is a white dot, that value is not included, a black dot is included

On this graph, that means -3 is not included but the value of 1 is so the domain is -3 < x < 1

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​(Since we start at an open circle where x=-3 and go right until we stop at a closed circle at x=1)

Multiple Choice

Is 5 a possible x-value for this function?

• yes

• no

Multiple Choice

Is 0 a possible x-value for this function?

• yes

• no

Multiple Choice

Is 2 a possible x-value for this function?

• no, because it has an open circle on it

• yes, because it has an open circle on it

Multiple Choice

Is -3 a possible x-value for this function?

• yes, because it has a closed circle on it

• yes, because it has an open circle on it

Multiple Choice

What is the range of this graph

• -5 < y < 4

• -5 < y < 0

• -3 < y < 2

Multiple Choice

Is -1 a possible x-value?

• Yes

• No

Multiple Choice

Is 0 a possible x-value?

• Yes

• No

Multiple Choice

What is the range of the graph?

• 1 ≤ y ≤ 5

• 1 < y < 5

Multiple Choice

What is the Domain?

• -3 < x ≤ 3

• -4 ≤ x < 5

Multiple Choice

What is the DOMAIN of this graph?

• -4 ≤ x ≤ 3

• -1 ≤ x ≤ 4

• 4 < x < 3

• -1 < x < 4

Multiple Choice

What is the range?

• -3 < y < 3

• -3 ≤ y ≤ 3

Multiple Choice

What is the DOMAIN of this graph?

Note: The graph starts with an open circle.

• x < -3

• x ≤ -3

• x > -3

• x ≥ -3

Multiple Choice

What is the Range?

• y ≥ 6

• y < 6

​When is a Relation a Function?

Function: Every input has exactly one output

--> ​Meaning: x cannot go to more than one y

​NOTE: Functions are a subset of Relations

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• ​Check if x repeats in the list of ordered pairs, table, or mapping

• ​Use the Vertical line test to check if x repeats in a graph

Multiple Choice

What is the definition of function?

• Has inputs and outputs

• Every input has only ONE output

• Inputs have different outputs every time

• x-values and y-values

Multiple Choice

• Function

• Not a Function

Multiple Choice

• Function

• Not a Function

Multiple Choice

• Function

• Not a Function

Multiple Choice

• Function

• Not a Function

Multiple Choice

• Function

• Not a Function

Multiple Choice

• Function

• Not a Function

Multiple Choice

• Function

• Not a Function

Multiple Choice

• Function

• Not a Function

​Make sure you wrote notes and examples in your notebook!

​We will be practicing this in class tomorrow.