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Chapter 2

Resource Masters

Consumable Workbooks

Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks. Study Guide and Intervention Workbook0-07-828029-X

Skills Practice Workbook0-07-828023-0

Practice Workbook0-07-828024-9

ANSWERS FOR WORKBOOKSThe answers for Chapter 2 of these workbooks can be found in the back of this Chapter Resource Masters booklet. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teacher, and families without charge; and be used solely in conjunction with GlencoeÕs Algebra 2.Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.

Send all inquiries to:

The McGraw-Hill Companies

8787 Orion Place

Columbus, OH 43240-4027

ISBN: 0-07-828005-2Algebra 2

Chapter 2 Resource Masters

2 3 4 5 6 7 8 9 10 066 11 10 09 08 07 06 05 04 03

Study Guide and Intervention

Relations and Functions

NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1

©Glencoe/McGraw-Hill57Glencoe Algebra 2

Lesson 2-1

Graph RelationsA relationcan be represented as a set of ordered pairs or as an equation; the relation is then the set of all ordered pairs ( x,y) that make the equation true. The domainof a relation is the set of all first coordinates of the ordered pairs, and the rangeis the set of all second coordinates. A functionis a relation in which each element of the domain is paired with exactly one element of the range. You can tell if a relation is a function by graphing, then using the vertical line test.If a vertical line intersects the graph at more than one point, the relation is not a function. Graph the equation y2x3 and find the domain and range. Does the equation represent a function?

Make a table of values to find ordered pairs that

satisfy the equation. Then graph the ordered pairs. The domain and range are both all real numbers. The graph passes the vertical line test, so it is function. Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function. 1. {(1, 3), (3, 5),2.{(3,4), (1, 0),3.{(0, 4), (3,2),

2, 5), (2, 3)} (2,2), (3, 2)} (3, 2), (5, 1)}

D {3,2, 1, 2}, D {1, 2, 3}, D {3, 0, 3, 5},

R {3, 5}; yes R {4,2, 0, 2}; no R {2, 1, 2, 4}; yes 4.yx 2

15.yx46.y3x2

D all reals, D all reals, D all reals,

R {yy1}; yes R all reals; yes R all reals; yes xy O xy O xy O xy O xy O xy O xy O xy 15 03 11 21
33

ExampleExample

ExercisesExercises

©Glencoe/McGraw-Hill70Glencoe Algebra 2

Parallel and Perpendicular Lines

Study Guide and Intervention (continued)

Slope NAME ______________________________________________ DATE______________ PERIOD _____2-32-3

In a plane, nonvertical lines with the

same slope are parallel. All vertical lines are parallel.xyO slope m slope m

In a plane, two oblique lines are perpendicularif

and only if the product of their slopes is 1. Any vertical line is perpendicular to any horizontal line.xyO slope m slope 1 m Are the line passing through (2, 6) and (2, 2) and the line passing through (3, 0) and (0, 4) parallel, perpendicular, or neither?

Find the slopes of the two lines.

The slope of the first line is 1.

The slope of the second line is .

The slopes are not equal and the product of the slopes is not 1, so the lines are neither parallel nor perpendicular. Are the lines parallel, perpendicular, or neither?

1.the line passing through (4, 3) and (1,3) and the line passing through (1, 2) and (1, 3)perpendicular

2.the line passing through (2, 8) and (2, 2) and the line passing through (0, 9) and (6, 0)

neither

3.the line passing through (3, 9) and (2,1) and the graph of y2xparallel

4.the line with x-intercept 2 and y-intercept 5 and the line with x-intercept 2 and

y-intercept 5 parallel

5.the line with x-intercept 1 and y-intercept 3 and the line with x-intercept 3 and

y-intercept 1 neither

6.the line passing through (2,3) and (2, 5) and the graph of x2y10perpendicular

7.the line passing through (4,8) and (6,4) and the graph of 2x5y5parallel

4 34 0

0 36 2

2 (2)

©Glencoe/McGraw-Hill72Glencoe Algebra 2

Find the slope of the line that passes through each pair of points.

1.(3,8), (5, 2)

2.(10,3), (7, 2)3.(7,6), (3,6)0

4.(8, 2), (8,1)undefined5.(4, 3), (7,2)6.(6,3), (8, 4)

Graph the line passing through the given point with the given slope.

7.(0,3),m38.(2, 1),m

9.(0, 2),m010.(2,3),m

Graph the line that satisfies each set of conditions.

11.passes through (3, 0), perpendicular12.passes through (3,1), parallel to a line

to a line whose slope is whose slope is 1 DEPRECIATIONFor Exercises 13Ð15, use the following information. A machine that originally cost $15,600 has a value of $7500 at the end of 3 y ears. The same machine has a value of $2800 at the end of 8 years.

13.Find the average rate of change in value (depreciation) of the machine between itspurchase and the end of 3 years.

$2700 per year

14.Find the average rate of change in value of the machine between the end of 3 years andthe end of 8 years.

$940 per year

15.Interpret the sign of your answers.It is negative because the value is decreasing.

xyO xyO 3 2 xO y xyO 4 5 xyO xyO 3 4 7 25
35
175
4

Practice (Average)

Slope NAME ______________________________________________ DATE______________ PERIOD _____

2-32-3

Write the letter for the correct answer in the blank at the right of each question.

1.Find the domain of the relation {(0, 0), (1, 1), (2, 0)}. Then determine

whether the relation is a function.

A.{0, 1, 0}; functionB.{0, 1, 0}; not a function

C.{0, 1, 2}; functionD.{0, 1, 2}; not a function1. 2. The table shows the annualized percent return of a mutual fund for several years. Find the range of the relation. Then determine whether the relation is a function. A.{20.9, 22.8, 20.0, 20.5}; not a functionB.{1, 3, 5, 10}; not a function C.{20.9, 22.8, 20.0, 20.5}; functionD.{1, 3, 5, 10}; function2. 3.

Find f(1) if f(x)3x5.

A.9B.8C.2D.23.

4.

Find f(0) if f(t)t

2 2t2.

A.2B.4C.0D.24.

5.

Which equation is linear?

A.xy60B.3x2y5

C.yx 2

3x1D.y

2 1x5. 6.

Which function is a linear function?

A.f(x)x

3 xB.g(s)14s

C.h(t)2t

1 t

D.f(r)r6.

7.

Write y4x7 in standard form.

A.4xy7B.4xy7 C.y4x7D.4xy77.

8.

Find the x-intercept of the graph of5x10y20.

A.2B.2C.4D.48.

9. Find the slope of the line that passes through (0, 2) and (8, 8). A.8B. 4 3 C. 3 4 D. 5 49.
10. If a line rises to the right, its slope is ___?____.

A.zeroB.positiveC.negativeD.undefined10.

11. What is the slope of a line that is perpendicular to the graph ofy2x5? A. 1 2 B. 1 2

C.2D.211.

12. Graph the line through (2, 3) that is parallel to the line with equation y1. Which point below also lies on that line?

A.(2, 9)B.(5, 3)C.(0, 1)D.(1, 4)12.

Chapter 2 Test, Form 1

NAME DATE PERIOD

SCORE

©Glencoe/McGraw-Hill99Glencoe Algebra 2

Assessment

22

Year13510

Percent Return20.9 22.8 20.0 20.5

Standardized Test Practice

Student Record Sheet(Use with pages 106-107 of the Student Edition.)

©Glencoe/McGraw-HillA1Glencoe Algebra 2

NAME DATE PERIOD

22

Answers

Select the best answer from the choices given and fill in the corresponding oval. 147
258
369
Solve the problem and write your answer in the blank. For Questions 11Ð17, also enter your answer by writing each number or symbol in a box. Then fill in the corresponding oval for that number or symbol.

10 12 14 16

11 13 15 17

Select the best answer from the choices given and fill in the corresponding oval.

18 20 22

19 21

DCBADCBA

DCBADCBADCBA

000

9999876543

2 1 8 7 6 5 43
2

1876543

2

1876543

2 1 000

999987654321876543

2

1876543

2

1876543

2 1 000

999987654321

8 7 6 5

432187654321876543

2 1 000

999987654321

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