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Chapter 2A1Glencoe Algebra 2

Answers

Answers(Anticipation Guide and Lesson 2-1)

STEP 1

Chapter 2

3

Glencoe Algebra 2

NAME ______________________________________________ DATE ____________ PERIOD _____ 2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Anticipation GuideLinear Relations and Functions

Before you begin Chapter 2

• Read each statement. ¥ Decide whether you Agree (A) or Disagree (D) with the statement. ¥ Write A or D in the first column OR if you are not sure whether you agree or disagree,write NS (Not Sure).

After you complete Chapter 2

• Reread each statement and complete the last column by entering an A or a D.¥ Did any of your opinions about the statements change from the first column?¥ For those statements that you mark with a D, use a piece of paper to write an example of

why you disagree.

STEP 2

STEP 1

STEP 2

A, D, or NS

Statement

A or D

1.

A function is any set of ordered pairs.

D 2.

If a vertical line intersects the graph of a relation in two or more points, then the relation is not a function.

A 3. A linear function is a function whose ordered pairs satisfy a linear equation. A 4.

The slope of a line is the change of x

-coordinates divided by the change of y -coordinates. D 5.

A vertical line has an undefined slope.

A 6.

Any two perpendicular lines have the same slope.

D 7.

A line written in the form y

mx b is said to be in slope-intercept form. A 8.

If a line has the equation

y 3 4( x

3), then (

2, 3) is a point on the line. D 9. A line of fit for the graph of a set of data passes through all data points on the graph. D 10. A scatter plot of a data set shows if there is a relationship between the data. A 11. The graph of a step function consists of line segments or rays that are not connected. A 12.

The graph of

y 2 x

4 is the same as the graph of the

line y 2 x 4. D

Chapter Resources

2-1Lesson 2-1

Chapter 2

5

Glencoe Algebra 2

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. NAME ______________________________________________ DATE ____________ PERIOD _____ 2-1

Lesson Reading GuideRelations and Functions

Get Ready for the LessonRead the introduction to Lesson 2-1 in your textbook.• Refer to the table. What does the ordered pair (8, 20) tell you?

For a deer, the

average longevity is 8 years and the maximum longevity is 20 years. • Suppose that this table is extended to include more animals. Is it possible to have an ordered pair for the data in which the first number is larger than the second?

Sample

answer: No, the maximum longevity must always be greater than theaverage longevity.

Read the Lesson

1. a. Explain the difference between a relation and a function.

Sample answer: A

relation is any set of ordered pairs. A function is a special kind ofrelation in which each element of the domain is paired with exactlyone element in the range.

b.

Explain the difference between domain and range.

Sample answer:The domain

of a relation is the set of all first coordinates of the ordered pairs.Therange is the set of all second coordinates.

2. a. Write the domain and range of the relation shown in the graph.D: { 3, 2,

1, 0, 3}; R: {

5,

4, 0, 1, 2, 4}

b.

Is this relation a function? Explain.

Sample answer: No, it is not a function

because one of the elements of the domain, 3, is paired with twoelements of the range.

Remember What You Learned

3.

Look up the words

dependent and independent in a dictionary. How can the meaning of these words help you distinguish between independent and dependent variables in afunction?

Sample answer:The variable whose values depend on, or aredetermined by, the values of the other variable is the dependent variable.

0, 4 3, 1

3, Ð4

Ð1, Ð5

Ð2, 0

Ð3, 2

)x y O

A1-A26 A2-02-873972 5/17/06 10:37 AM Page A1

Chapter 2A2Glencoe Algebra 2

Answers(Lesson 2-1)

Example

Study Guide and InterventionRelations and Functions

Chapter 2

6

Glencoe Algebra 2

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. NAME ______________________________________________ DATE ____________ PERIOD _____ 2-1

Graph Relations

A relation can 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 domain of a relation is the set of all first coordinates of the ordered pairs, and the range is the set of all second coordinates. A function is 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 thevertical line test

. If a vertical line intersects the graph at more than one point, the relation is not a function.

Graph the equation

y 2 x

3 and find the domain and range. Is

the equation discrete or continuous? 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. Theequation can be graphed by line, so it is continuous. Thegraph passes the vertical line test, so it is a function.Graph each relation or equation and find the domain and range. Next determine ifthe relation is discrete or continuous. Then determine whether the relation orequation 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}; R 4,

2, 0, 2}; R

2, 1, 2, 4};

discrete; yes discrete; no discrete; yes 4. y x 2 1 5. y x 4 6. y 3 x 2 D all reals, D all reals, D all reals, R y y 1}; R all reals; R all reals; continuous; yes continuous; yes continuous; yes x y O x y O x y O x y O x y O x y O x y O xy 1 5 0 3 1 1 2133

Exercises

Lesson 2-1

Equations of Functions and Relations

Equations that represent functions are

often written in functional notation . For example, y 10 8 x can be written as f x 10 8 x . This notation emphasizes the fact that the values of y , the dependent variable , depend on the values of x , the independent variable

To evaluate a function, or find a functional value, means to substitute a given value in thedomain into the equation to find the corresponding element in the range.

Given the function

f x x 2 2 x , find each value. a. f (3) f x x 2 2 x

Original function

f (3) 3 2 2(3)

Substitute.

15

Simplify.

b. f (5 a f x x 2 2 x

Original function

f (5 a (5 a 2 2(5 a

Substitute.

25
a 2 10 a

Simplify.

Find each value if

f x 2 x 4. 1. f (12) 20 2. f (6) 8 3. f (2 b 4 b 4

Find each value if

g x x 3 x 4. g (5) 120
5. g 2) 6 6. g (7 c 343
c 3 7 c

Find each value if

f x 2 x and g x 0.4 x 2 1.2. 7. fquotesdbs_dbs14.pdfusesText_20