Exercises. Bottled Water Consumption. U. S. Paper Recycling

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1 Eercises Use the graph of each function to estimate the indicated function values. Then confirm the estimate algebraicall. Round to the nearest hundredth, if necessar. (Eample 1) g() = g() = a. g (6) b. g (1) c. g (19) a. g (-) b. g (1) c. g () 3. f() 1 = + P (t) 3 if t < = t 1 if t a. f (-) b. f (-3) c. f () a. P(-6) b. P() c. P(9) f() = - 1 h() = _ - 3. WATER Bottled water consumption from 1977 to 6 can be modeled using f () = , where represents the number of ears since (Eample 1) Millions of Gallons Bottled Water Consumption Years Since 1977 a. Use the graph to estimate the amount of bottled water consumed in 199. b. Find the 199 consumption algebraicall. Round to the nearest ten million gallons. c. Use the graph to estimate when water consumption was 6 billion gallons. Confirm algebraicall. Use the graph of h to find the domain and range of each function. (Eample ) a. f (-3) b. f (.5) c. f () a. h(-1) b. h(1.5) c. h() = h () = h () 7. RECYLING The quantit of paper reccled in the United States in thousands of tons from 1993 to 7 can be modeled b p() = , where is the number of ears since (Eample 1) Reccled Paper (Thousands of Tons) U. S. Paper Reccling Years Since 1993 a. Use the graph to estimate the amount of paper reccled in 1993, 1999, and 6. Then find each value algebraicall. b. Use the graph to estimate the ear in which the quantit of paper reccled reached 5, tons. Confirm algebraicall = h () = h() = h () = h() 19

2 15. ENGINEERING Tests on the phsical behavior of four metal specimens are performed at various temperatures in degrees Celsius. The impact energ, or energ absorbed b the sample during the test, is measured in joules. The test results are shown. (Eample ) Use the graph of each equation to test for smmetr with respect to the -ais, -ais, and the origin. Support the answer numericall. Then confirm algebraicall. (Eample 5). 5. Impact Energ (J) Impact Test Results.5 + = = = - a. State the domain and range of each function. b. Use the graph to estimate the impact energ of each metal at C. Use the graph of each function to find its -intercept and zero(s). Then find these values algebraicall. (Eamples 3 and ) Temperature ( C) 16. $PQQFS. 1.5 "MVNJOJVN 1. ;JOD.5 UFFM = =_ 3 1 = -_ f () = - 1 f () = f () = = f () = 6 f () = f () = ( - 6) + = 6 GRAPHING CALCULATOR Graph each function. Analze the graph to determine whether each function is even, odd, or neither. Confirm algebraicall. If odd or even, describe the smmetr of the graph of the function. (Eample 6) 3. 36( + ) - 16( - 3) = f () = = - f () = f () = f () = g () = """ 37. h() = """ h() = f () = 3. f () = _ 1. g () = _ Lesson 1- Analzing Graphs of Functions and Relations

3 Use the graph of each function to estimate the indicated function values.. 3. f() g() a. f (-) b. f (-6) c. f () a. g (-) b. g (-6) c. g (-). FOOTBALL A running back s rushing ards for each game in a season are shown. Rushing Yards Season Rushing Yards Game a. State the domain and range of the relation. b. In what game did the plaer rush for no ards? 5 PHONES The number of households h in millions with onl wireless phone service from 1 to 5 can be modeled b h() = , where represents the number of ears after 1. Millions of Households Wireless Onl Households Years Since 1 6. FUNCTIONS Consider f () = n. a. Use a graphing calculator to graph f () for values of n in the range 1 n 6, where n. b. Describe the domain and range of each function. c. Describe the smmetr of each function. d. Predict the domain, range, and smmetr for f () = 35. Eplain our reasoning. 7. PHARMACOLOGY Suppose the number of milligrams of a pain reliever in the bloodstream hours after taking a dose is modeled b f () = b. State the relevant domain. Eplain our reasoning. c. What was the approimate maimum amount of pain reliever, in milligrams, that entered the bloodstream? GRAPHING CALCULATOR Graph and locate the zeros for each function. Confirm our answers algebraicall.. f () = _ h() = g () = -1 + _ 9. f () = _ h() = g () = 6_ TELEVISION The percent of households h with basic cable for the ears 19 through 6 can be modeled using h() = , 19 6, where represents the number of ears after 19. b. What percent of households had basic cable in 1999? Round to the nearest percent. c. For what ears was the percent of subscribers greater than 65%? Use the graph of f to find the domain and range of each function f() f() a. State the relevant domain and approimate the range. b. Use the graph to estimate the number of households with onl wireless phone service in 3. Then find it algebraicall. c. Use the graph to approimate the -intercept of the function. Then find it algebraicall. What does the -intercept represent? d. Does this function have an zeros? If so, estimate them and eplain their meaning. If not, eplain wh f() f() 1

4 59. POPULATION The percent population change from 193 to 19, 19 to 195, and so on, for a certain U.S. cit from 193 to can be modeled b f () = , where is the number of ears since 193. = f() [-5, 1] scl: 15 b [-3, 7] scl: 1 a. State the relevant domain and estimate the range for this domain. b. Use the graph to approimate the -intercept. Then find the -intercept algebraicall. What does the -intercept represent? c. Find and interpret the zeros of the function. d. Use the model to determine what the percent population change will be in. Does this value seem realistic? Eplain our reasoning. 6. STOCK MARKET The percent p a stock price has fluctuated in one ear can be modeled b p() = , where is the number of months since Januar. b. State the relevant domain and estimate the range. c. Use the graph to approimate the -intercept. Then find the -intercept algebraicall. What does the -intercept represent? d. Find and interpret an zeros of the function. 61. MULTIPLE REPRESENTATIONS In this problem, ou will investigate the range values of f () = 1_ - as approaches. a. TABULAR Cop and complete the table below. Add an additional value to the left and right of f ( ) b. ANALYTICAL Use the table from part a to describe the behavior of the function as approaches. c. GRAPHICAL Graph the function. Does the graph support our conjecture from part b? Eplain. d. VERBAL Make a conjecture as to wh the graph of the function approaches the value(s) found in part c, and eplain an inconsistencies present in the graph. GRAPHING CALCULATOR Graph each function. Analze the graph to determine whether each function is even, odd, or neither. Confirm algebraicall. If odd or even, describe the smmetr of the graph of the function. 6. f () = g (n) = n h() = f (g) = g g () = h() = h(b) = b - b 3-13 b + 1b + H.O.T. Problems Use Higher-Order Thinking Skills OPEN ENDED Sketch a graph that matches each description. 69. passes through (-3, ), (-, ), (-5, ), and (-, 1) and is smmetric with respect to the -ais 7. passes through (, ), (, 6), (3, 1), and (, ) and is smmetric with respect to the -ais 71 passes through (-3, -1), (-, -9), and (-1, -3) and is smmetric with respect to the origin 7. passes through (, -16), (6, -1), and (, -) and represents an even function 73. WRITING IN MATH Eplain wh a function can have, 1, or more -intercepts but onl one -intercept. 7. CHALLENGE Use a graphing calculator to graph f () = + 3 -, and predict its domain. Then confirm the domain algebraicall. Eplain our reasoning. REASONING Determine whether each statement is true or false. Eplain our reasoning. 75. The range of f () = n, where n is an integer, is {, }. 76. The range of f () = n, where n is an integer, is {, }. 77. All odd functions are also smmetric with respect to the line = An even function rotated 1n about the origin, where n is an integer, remains an even function. REASONING If a() is an odd function, determine whether b() is odd, even, neither, or cannot be determined. Eplain our reasoning. 79. b() = a(-). b() = -a() 1. b() = [a() ]. b() = a( ) 3. b() = [a() ] 3 REASONING State whether a graph with each tpe of smmetr alwas, sometimes, or never represents a function. Eplain our reasoning.. smmetric with respect to the line = 5. smmetric with respect to the line = 6. smmetric with respect to the line = 7. smmetric with respect to both the - and -aes. WRITING IN MATH Can a function be both even and odd? Eplain our reasoning. Lesson 1- Analzing Graphs of Functions and Relations

5 Spiral Review Find each function value. (Lesson 1-1) _ 9. g () = h() = p() = a. g () a. h(-9) a. p(3) b. g (-) b. h(3) b. p( ) c. g (1 + 3n) c. h( + m) c. p( + 1) 9. State the relation in the table as a set of ordered pairs. Then state the domain and range of the relations. (Lesson 1-1) 93. What are the domain and the range of the relation {(1, 5), (. 6), (3, 7), (, )}? Is the relation a function? Eplain. (Lesson 1-1) _ 9. Find g(-) if g() = (Lesson 1-1) X Y Given that is an integer, state the relation representing = - 3 and - 3 b making a table of values. Then graph the ordered pairs of the relation. (Lesson 1-1) 96. FINANCE The formula for the simple interest earned on an investment is I =prt, where I is the interest earned, p is the principal, r is the interest rate, and t is the time in ears. Assume that $5 is invested at an annual Interest rate of % and that interest is added to the principal at the end of each ear. (Lesson 1-1) a. Find the amount of interest that will be earned each ear for five ears. b. State the domain and range of the relation. c. Is this relation a function? Wh or wh not? 97. INTERNATIONAL BUSINESS Value-added ta, VAT, is a ta charged on goods and services in European countries. Man European countries offer refunds of some VAT to non-resident based businesses. VAT is included in a price that is quoted. That is, if an item is marked as costing $1, that price includes the VAT. a. Suppose an American compan has operations in The Netherlands, where the VAT is 17.5%. Write a function for the VAT amount paid v(p) if p represents the price including the VAT. b. In The Netherlands, foreign businesses are entitled to a refund of % of the VAT on automobile rentals. Write a function for the refund an American compan could epect r(v) if v represents the VAT amount. c. Write a function for the refund epected on an automobile rental r(p) if the price including VAT is p. d. Find the refunds due on automobile rental prices of $3.1, $5.6, and $ Skills Review for Standardized Tests 9. SAT/ACT In the figure, if n is a real number greater than 1, what is the value of in terms of n? A n n B n - 1 D n - 1 C n + 1 E n REVIEW Which inequalit describes the range of f () = + 1 over the domain - < < 3? F 5 < 9 H 1 < < 9 G < < 1 J 1 < 1 1. Which of the following is an even function? A f () = B g () = C m() = D h() = Which of the following is the domain of g () = _ - 16? F (-, ) (, 16) (16, ) G (-, ] [16, ) H (-, -1) (-1, ) J (-, -) (-, ) (, ) 3