Answers (Anticipation Guide and Lesson 2-1)

1 Chapter 2A1 Glencoe Algebra 2 AnswersAnswers (Anticipation Guide and Lesson 2-1)STEP 1 Chapter 23 Glencoe Algebra 2 NAME _____ DATE _____ PERIOD _____2 copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, GuideLinear Relations and FunctionsBefore 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?

2 For those statements that you mark with a D, use a piece of paper to write an example ofwhy you 2 STEP 1 STEP 2A, D, or NSStatementA or function is any set of ordered a vertical line intersects the graph of a relation in two or more points, then the relation is not a linear function is a function whose ordered pairs satisfy a linear slope of a line is the change of x-coordinates divided by the change of vertical line has an undefined two perpendicular lines have the same line written in the form y mx bis said to be in slope-intercept a line has the equation y 3 4(x 3), then ( 2, 3) is a point on the line.

3 Line of fit for the graph of a set of data passes through all data points on the scatter plot of a data set shows if there is a relationship between the graph of a step function consists of line segments or rays that are not graph of y 2x 4 is the same as the graph of the line y 2x Resources2-1 Lesson 2-1 Chapter 25 Glencoe Algebra 2 copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, _____ DATE _____ PERIOD _____2-1 Lesson Reading GuideRelations and FunctionsGet 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?

4 For a deer, theaverage 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 anordered pair for the data in which the first number is larger than the second?Sampleanswer: No, the maximum longevity must always be greater than theaverage the Lesson1. the difference between a relation and a answer: Arelation 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 the difference between domain and answer: The domainof a relation is the set of all first coordinates of the ordered pairs.

5 Therange is the set of all second the domain and range of the relation shown in the : { 3, 2, 1, 0, 3}; R: { 5, 4, 0, 1, 2, 4} this relation a function? answer: No, it is not a functionbecause one of the elements of the domain, 3, is paired with twoelements of the What You up the words dependentand independentin a dictionary. How can the meaning ofthese 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, 4)( 1, 5)( 2, 0)( 3, 2)xyOA1-A26 A2-02-873972 5/17/06 10:37 AM Page A1 Chapter 2A2 Glencoe Algebra 2 Answers ( Lesson 2-1)ExampleStudy Guide and InterventionRelations and FunctionsChapter 26 Glencoe Algebra 2 copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, _____ DATE _____ PERIOD _____2-1 Graph RelationsArelationcan be represented as a set of ordered pairs or as anequation.

6 The relation is then the set of all ordered pairs (x, y) that make the equation domainof a relation is the set of all first coordinates of the ordered pairs, and therangeis the set of all second a relation in which each element of the domain is paired with exactly oneelement 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, therelation is not a the equation y 2x 3 and find the domain and range. Isthe equation discrete or continuous? Does the equation represent a function?Make a table of values to find ordered pairs that satisfy the equation.

7 Then graph the ordered 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 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 {(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; yesdiscrete; nodiscrete; x2 x 3x 2D all reals,D all reals,D all reals,R {y y 1};R all reals;R all reals;continuous; yescontinuous; yescontinuous; yesxyOxyOxyOxyOxyOxyOxyOxy 1 50 31 12133 ExercisesLesson 2-1 Equations of Functions and RelationsEquations that represent functions areoften written in functional notation.

8 For example, y 10 8xcan be written as f(x) 10 8x. This notation emphasizes the fact that the values of y, the dependentvariable, depend on the values of x, the independent 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 the function f(x) x2 2x, find each (3)f(x) x2 2xOriginal functionf(3) 32 2(3)Substitute. (5a)f(x) x2 2xOriginal functionf(5a) (5a)2 2(5a)Substitute. 25a2 each value if f(x) 2x (12) (6) (2b) 4b 4 Find each value if g(x) x3 (5) ( 2) (7c)343c3 7cFind each value if f(x) 2x and g(x) ( ) ( 8) (3) ( ) (4a)8a (10) (200) f(x) 2x2 the values of f(2) and f(5).

9 F(2) 7,f(5) the values of f(2) f(5) and f(2 5).f(2) f(5) 343,f(2 5) 1992 31 3b2 10b 21 2a1 42 xStudy Guide and Intervention (continued)Relations and FunctionsChapter 27 Glencoe Algebra 2 copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, _____ DATE _____ PERIOD _____2-1 ExampleExercisesA1-A26 A2-02-873972 5/17/06 10:37 AM Page A2 Chapter 2A3 Glencoe Algebra 2 AnswersAnswers( Lesson 2-1)Chapter 28 Glencoe Algebra 2 NAME _____ DATE _____ PERIOD _____2-1 copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, PracticeRelations and FunctionsDetermine whether each relation is a function.

10 Write yesor 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 {(2, 3), (2, 4), (2, 1)}6.{(2, 6), (6, 2)}D {2}, R { 3, 1, 4}; discrete; no D {2, 6}, R {2, 6}; discrete; yes7.{( 3, 4), ( 2, 4), ( 1, 1), (3, 1)} 2D { 3, 2, 1, 3},D { 2}, R all reals; discrete; no R { 1, 4}; discrete; yesFind each value if f(x) 2x 1 and g(x) 2 (0) (12) (4) ( 2) ( 1) (d)2d 1xyO( 2, 4)( 3, 4)( 1, 1)(3, 1)xyO(2, 6)(6, 2)xyO(2, 4)(2, 1)(2, 3)xyOxyOxy122436315 DomainRange10020030050100150 DomainRange2-1 Lesson 2-1 Determine whether each relation is a function.