1. Cornell Notes Section 1.2 Day 1 Section 1.2 Day 2 Section 1.4 Day 1
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Section 1.2 Day 2
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2. Cornell Notes Section 1.2 Day 2 Section 1.4 Day 1 Section 1.6 Day 1
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3. Cornell Notes Section 1.4 Day 1 Section 1.6 Day 1 Section 1.6 Day 2
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4. Section 1.6 Relations
Algebra 1

5. Learning Targets
Define the vocabulary terms: coordinate system, x-axis, y-axis, origin, ordered pair, x-coordinate, y-coordinate, relation, mapping, domain, range, independent variable, and dependent variable
Verbalize the relationships between ordered pairs, tables, graphs, mappings, and relations
Determine the domain and range of a relation
Construct different representations of relations given one representation
Identify the independent and dependent variables of a relation
Describe the pattern of a relation in a context
Construct a graph of a relation given a verbal description of the relation

6. Coordinate System Constructs the coordinate system
Ordered Pair
Y-Axis
Each point on the coordinate plane in the form (𝑥,𝑦)
Constructs the coordinate system
X-Axis
Origin
(0,0)
In (2, 3), 2 is the x-coordinate and 3 is the
y-coordinate
Point where axes intersect
(2,3)

7. Relation Relation Definition:
A set of pairs of input and output values
Characteristics:
Multiple Representations:
Ordered pairs
Table
Graph
Equation
Words
Mapping Diagram
Relation
Examples:
4, 7 , 3, 2 , 0,0 , −1,−4
Input: X 𝟎 −𝟐 𝟑
Output: Y 1 4 7

8. Relation Representations
Ordered Pairs:
1, 2 , 3, −1 , 5, 6 , 0,−9 , −3,6
Table:
X: Input
Y: Output X 𝟎 −𝟐 𝟑 Y 1 4 7
Graph:
X-Coordinate:
Input/Horizontal
Y-Coordinate:
Output/Vertical
Mapping Diagram:
Maps inputs to outputs −2 −1 1 4 6 8 9

9. Example 1: Multiple Representations
Express the relation 2, 5 , 5, −2 , −2, 3 , −1, −2 as a table, graph, and a mapping X Y −2 3 −1 2 5 −2 −1 2 5 3 −2 5

10. Domain & Range Range: The output values of a relation
Domain: The input values of a relation.
EX: The x-coordinate in ordered pairs, tables, and graphs.
EX: The inputs of the mapping diagram.
Range: The output values of a relation
EX: The y-coordinate in ordered pairs, tables, and graphs
EX: The outputs of the mapping diagram

11. Domain & Range: Example 2: Ordered Pairs
Find the domain and range of the following relation
{ 3, 4 , −2, 1 , 6, 5 , 9, −10 , −5, −7 }
Domain (Input, x-values): −5, −2, 3, 6, 9
Range (Output, y-values): {−10, −7, 1, 4, 5}

12. Domain & Range: Example 3: Tables
Find the domain and range of the following relation X Y −4 3 5 −2 7 X Y −4 3 5 −2 7 X Y −4 3 5 −2 7
Domain
(Input, x-values)
{𝟎, 𝟑, 𝟓, 𝟕}
Range
(Output, y-values)
{−𝟒, −𝟐, 𝟎, 𝟓}

13. Domain & Range: Example 4: Mapping Diagram
Find the domain and range of the following relation
Domain
(Input, x-values)
{−𝟕, −𝟏, 𝟒}
Range
(Output, y-values)
{−𝟗, 𝟎, 𝟑, 𝟏𝟖} −7 −1 4 −7 −1 4 3 18 −9 3 18 −9

14. Domain & Range: Example 5: Graph - Level 1
Find the domain and range of the following relation
Domain
(Input, x-values)
{−𝟓, −𝟐, 𝟎, 𝟐, 𝟒}
Range
(Output, y-values)
{−𝟖, −𝟒, 𝟏, 𝟑, 𝟓}

15. Domain & Range: Example 6: Graph - Level 2
Find the domain and range of the following relation
Domain
(Input, x-values)
{ −𝟔, −𝟏 &[𝟏,𝟒]}
Closed Brackets
All values between and including the end points
Range
(Output, y-values)
{ −𝟒,𝟎 & 𝟑}

16. Domain & Range: Example 7: Graph - Level 2
Find the domain and range of the following relation
Open Brackets
All values between and NOT including the end points
Range
(Output, y-values)
{[𝟏, 𝟔)}
Or 𝟏≤𝒚<𝟔
Domain
(Input, x-values)
{(−𝟕,𝟓]}
Or −𝟕<𝒙≤𝟓

17. Domain & Range: Example 8: Graph - Level 3
Find the domain and range of the following relation
Domain
(Input, x-values)
(−∞,∞)
Or −∞<𝒙<∞
Or All Real #s
Range
(Output, y-values)
{[−𝟑, ∞)}
Or −𝟑≤𝒚<∞

18. Domain & Range: Example 9: Graph - Level 3
Find the domain and range of the following relation
Domain
(Input, x-values)
[−𝟒,∞)
Or −𝟒≤𝒙<∞
Range
(Output, y-values)
{[𝟏, ∞)}
Or 1≤𝒚<∞

19. Domain & Range Example 10
Come up with a relation in a Mapping Diagram form that has the following Domain: {−𝟏𝟏 𝟎, 𝟏, 𝟐𝟓}
There are many possible answers
The key is that the input circle must only contain the numbers {−𝟏𝟏 𝟎, 𝟏, 𝟐𝟓}.
The output doesn’t matter
One possible answer:
−11 1 25 −4 −2

20. Domain & Range Example 11
Come up with a relation in an Ordered Pair form that has the following Range: {−𝟏𝟒, −𝟐, 𝟏𝟕, 𝟑𝟗}
There are many possible answers
The key is that all the y-values must only be the numbers {−𝟏𝟒, −𝟐, 𝟏𝟕, 𝟑𝟗}
The x-values don’t matter
One possible example: { 𝟎, −𝟏𝟒 , 𝟏, −𝟐 , 𝟐, 𝟏𝟕 , 𝟑, 𝟑𝟗 }

21. Independent & Dependent Variables
- The number of pickles you can make
- The amount of money raised
Dependent Variable:
The output values of a relation (y-values).
It relies on the independent variable.
Dependent variable
Independent Variable:
The input values of a relation (x-values).
Changing the independent variables
Independent Variable:
- The number of cucumbers you have
- The number of cookies baked
Causes change in the

22. Example 12: Independent/Dependent Variables
Identify the independent and dependent variables for each relation
A)The dance committee is selling tickets to the Fall Ball. The more tickets that they sell, the greater the amount of money they can spend for decorations.
B) The air pressure inside a tire increased with the temperature
C) The greater the number of hours driving, the greater the total distance traveled.
tickets
money
air pressure
temperature
hours
distance

23. Example 13: Graph Analysis
Independent Variable: Time
Dependent Variable: Distance
Origin-A: Rider is biking at a constant pace
A-B: Time is increasing as distance is constant. Rider has stopped moving
B-After: Rider continues to bike at a constant pace
Answer the following questions for the graph:
A) What is the independent and dependent variable?
B) Describe what is happening during the bike ride from the origin to point A, from point A to point B, and after point B

24. Example 14: Graph Construction
Create a graph that describes the height of a person jumping on a trampoline over a 5 minute period.
Be sure to create a realistic situation and describe what is happening in your graph. There are many situations
One example:

25. Exit Ticket – For Feedback
Find the Domain and Range of the following:
1) −2, 0 , 4, −2 , 1, 1 , 5, 9 2)
3) Identify the independent and dependent variable.
A teacher tested different types of teaching (reading, lecture, video, lab, etc.) to determine which helps students score higher on the tests. 1 2 7
−10 −1 12