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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD Lesson 1-6

Chapter 1 37 Glencoe Algebra 1

Study Guide and Intervention

Relations

1-6 Represent a Relation A relation is a set of ordered pairs. A relation can be represented by a set of ordered pairs, a table, a graph, or a mapping . A mapping illustrates how each element of the domain is paired with an element in the range. The set of first numbers of the ordered pairs is the domain . The set of second numbers of the ordered pairs is the range of the relation. a. Express the relation {(1, 1), (0, 2), (3, -2)} as a table, a graph, and a mapping. x y1 1 0 2 3 -2

A1-SG04-01-03-827728xy

O XY 1 0 312
2

A1-SG04-03-02A-827728

b. Determine the domain and the range of the relation. The domain for this relation is {0, 1, 3}. The range for this relation is {

2, 1, 2}.

Exercises

1A. Express the relation

2 1 3 , 3), (4, 3)} as a table, a graph, and a mapping

1B. Determine the domain and the range of the relation.Example

A1-SG04-01-05-827728xy

O XY-2 3 4-1 3

A1-SG04-03-04A-827728

x y 2-1 3 3 4 3 domain

2, 3, 4}

range 1, 3} Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Chapter 1 38 Glencoe Algebra 1

Graphs of a Relation The value of the variable in a relation that is subject to choice is called the independent variable . The variable with a value that is dependent on the value of the independent variable is called the dependent variable . These relations can be graphed without a scale on either axis, and interpreted by analyzing the shape.

The graph below

represents the height of a football after it is kicked downfield. Identify the independent and the dependent variable for the relation. Then describe what happens in the graph.

The independent variable is time, and the

dependent variable is height. The football starts on the ground when it is kicked. It gains altitude until it reaches a maximum height, then it loses altitude until it falls to the ground.

A1-SG01-08-01-827725

TimeHeight

The graph below

represents the price of stock over time.

Identify the independent and

dependent variable for the relation.

Then describe what happens in the

graph.

The independent variable is time and the

dependent variable is price. The price increases steadily, then it falls, then increases, then falls again.

A1-SG01-08-02-827725

TimePrice

Exercises

Identify the independent and dependent variables for each relation. Then describe what is happening in each graph.

1. The graph represents the speed of a car as it travels to the grocery

store.

2. The graph represents the balance of a savings account over time.

3. The graph represents the height of a baseball after it is hit.

A1-SG01-08-05-827725

TimeHeight

A1-SG01-08-04-827725

TimeAccount

Balance

(dollars)

A1-SG01-08-03-827725

TimeSpeed

Study Guide and Intervention (continued)

Relations

1-6

Example 1Example 2

Ind: time; dep: speed. The car starts from a standstill, accelerates, then travels at a constant speed for a while.Then it slows down and stops. Ind: time; dep: balance. The account balance has an initial value then it increases as deposits are made. It then stays the same for a while, again increases, and lastly goes to 0 as withdrawals are made. Ind: time; dep: height. The ball is hit a certain height above the ground. The height of the ball increases until it reaches its maximum value, then the height decreases until the ball hits the ground.quotesdbs_dbs20.pdfusesText_26