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You solved equations with one or two variables. (Lesson 1–5). Represent relations. Interpret graphs of relations. Then/Now. coordinate system. relation domain range independent variable dependent variable. x - and y -axes origin ordered pair x - and y -coordinates. Vocabulary.

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Then/Now

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Then now

You solved equations with one or two variables. (Lesson 1–5)

  • Represent relations.

  • Interpret graphs of relations.

Then/Now


Vocabulary

  • coordinate system

  • relation

  • domain

  • range

  • independent variable

  • dependent variable

  • x- and y-axes

  • origin

  • ordered pair

  • x- and y-coordinates

Vocabulary


Example 1

A. Express the relation {(4, 3), (–2, –1), (2, –4), (0, –4)} as a table, a graph, and a mapping.

Representations of a Relation

Table List the x-coordinates in the first column and the corresponding y-coordinates in the second column.

Example 1


Example 11

Graph Graph each ordered pair on a coordinate plane.

Representations of a Relation

Example 1


Example 12

MappingList the x-values in the domain and the y-values in the range. Draw an arrow from the x-value to the corresponding y-value.

Domain

Range

Representations of a Relation

Example 1


Example 13

B. Determine the domain and range for the relation {(4, 3), (–2, –1), (2, –4), (0, –4)}.

Representations of a Relation

Example 1


Example 14

A

B

C

D

A.C.

B.D.

A. Express the relation {(3, –2), (4, 6), (5, 2), (–1, 3)} as a mapping.

Example 1


Example 15

A

B

C

D

B. Determine the domain and range of the relation {(3, –2), (4, 6), (5, 2), (–1, 3)}.

  • D = {–1, 3, 4, 5}; R = {–2, 2, 3, 6}

  • D = {–2, 2, 3, 6}; R = {–1, 3, 4, 5}

  • D = {–1, 3}; R = {–2, 2}

  • D = {4}; R = {4}

Example 1


Example 2

Independent and Dependent Variables

A. CLIMATEIn warm climates, the average amount of electricity used rises as the daily average temperature increases, and falls as the daily average temperature decreases. Identify the independent and the dependent variables for this function.

Example 2


Example 21

Independent and Dependent Variables

B. The number of calories you burn increases as the number of minutes that you walk increases. Identify the independent and the dependent variables for this function.

Example 2


Example 22

A

B

C

D

A. In a particular club, as membership dues increase, the number of new members decreases. Identify the independent and dependent variable in this function.

  • The number of new members is the independent variable. The dues is the dependent variable.

  • Membership dues is the independent variable. Number of new members is the dependent variable.

  • C.x is the independent. y is the dependent.

  • D.Both are independent.

Example 2


Example 23

A

B

C

D

B. The area of a square increases as the length of a side increases. Identify the independent and dependent variable in this function.

A. The length of the side is independent, and the the area of the square is dependent.

B. The area is independent, and the side length is dependent.

C.Both variables are independent.

D.Both are dependent.

Example 2


Example 3

Analyze Graphs

The graph represents the temperature in Ms. Ling’s classroom on a winter school day. Describe what is happening in the graph.

Example 3


Example 31

A

B

C

D

The graph below represents Macy’s speed as she swims laps in a pool. Describe what is happening in the graph.

A.Macy is doing bobs.

B.Macy’s speed increases as she crosses the length of the pool, but then decreases to zero when she turns around at the end of each lap.

C.Macy is swimming at a constant speed.

D.Macy’s speed continues to decrease.

Example 3


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