INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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### Relations

• A relation is a set of ordered pairs. It can be represented as a table, a graph, or a mapping.
• The domain of a relation is the set of values given by the first terms of the ordered pairs. The range is the set of values given the second terms.
• The inverse of a relation R is the relation obtained by interchanging the coordinates in the ordered pairs of R. The domain of the inverse of R is the range of R and the range of the inverse of R is the domain of R.

### Relations

Let the relation R = { (1,1),(4,2),(5,6),(3,0)} . Represent R as a table and as a graph
• Find the x and y values
•  x
 line
 1
 4
 5
 3
 y
 line
 1
 2
 6
 0
• Chart the values
Let the relation R = { ( − 1,9.5),(5,0),( − 3, − 6),(8.5, − 7)} . Represent R as a table and as a graph
• Find the x and y values
•  x
 line
 − 1
 5
 − 3
 8.5
 y
 line
 9.5
 0
 − 6
 − 7
• Chart the values
Determine the values of the relation R from the figure
• Find the x and y values
•  x
 line
 − 1
 − 2
 − 3
 5
 y
 line
 − 1
 4
 2
 7
• Create the set from the coordinate pairs
R = { ( − 1, − 1),( − 2,4),( − 3,2),(5,7)}
Determine the values of the relation R from the figure
• Find the x and y values
 x
 line
 − 7
 − 2
 2
 6
 y
 line
 3
 − 2
 5
 − 10

• Create the set from the coordinate pairs
R = { ( − 7,3),( − 2, − 2),(2,5),( − 6,10)}
The relation R is described by the following table. Find the domain and range of R.
 x
 line
 − 10
 1
 3
 5
 y
 line
 3
 − 2
 5
 − 10
Domain correspond to x values and y values correspond to the range
Domain = { − 10,1,3,5}
Range = { 3, − 2,5, − 10}
The relation R is described by the following table. Find the domain and range of R.
 x
 line
 2
 4
 5
 − 9
 y
 line
 1
 − 2
 − 4
 3
Domain correspond to x values and y values correspond to the range
Domain = { 2,4,5, − 9}
Range = { 1, − 2, − 4, − 3}
Determine the domain and range of the relation R represented by the graph
Domain correspond to x values and y values correspond to the range
Domain = { − 9, − 7, − 1,0}
Range = { 9,8, − 2, − 4}
Determine the domain and range of the relation R represented by the graph
Domain correspond to x values and y values correspond to the range
Domain = { − 4,0,2,7}
Range = { 4, − 3,2,0}
The relation R is given by the following table. Write the inverse of R as a list of ordered pairs,then find the domain and range of the inverse of R.
 x
 line
 − 2
 − 1
 0
 5
 y
 line
 9
 8
 7
 6
• The inverse has the y and x values switched
• Inverse of R = { (9, - 2),(8, - 1),(7,0),(6,5)}
Domain correspond to x values and y values correspond to the range of the inverse
Domain = { 9,8,7,6}
Range = { − 2, − 1,0,5}
The relation R is given by the following table. Write the inverse of R as a list of ordered pairs, then find the domain and range of the inverse of R.
 x
 line
 − 10
 3
 − 4
 7
 y
 line
 4
 0
 − 2
 − 6
• The inverse has the y and x values switched
• Inverse of R = { (4, - 10),(0,3),( - 2, - 4),( - 6,7)}
Domain correspond to x values and y values correspond to the range of the inverse
Domain = { 9,8,7,6}
Range = { − 10,3, − 4,7}

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Relations

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Definition 0:04
• Relation
• Table
• Set of Ordered Pairs
• Graph
• Domain and Range 2:40
• Example: Relation
• Example: Broader Cases
• Inverse of a Relation 4:42
• Example
• Example 1: Relation as Table/Graph 6:15
• Example 2: Domain and Range 8:41
• Example 3: Table, Graph, Domain, Range 10:36
• Example 4: Inverse of a Relation 13:36