Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world

Transcription

1

2 Pearson Education Limited Edinburgh Gate Harlow Esse CM0 JE England and Associated Companies throughout the world Visit us on the World Wide Web at: Pearson Education Limited 0 All rights reserved. No part of this publication ma be reproduced, stored in a retrieval sstem, or transmitted in an form or b an means, electronic, mechanical, photocoping, recording or otherwise, without either the prior written permission of the publisher or a licence permitting restricted coping in the United Kingdom issued b the Copright Licensing Agenc Ltd, Saffron House, 6 0 Kirb Street, London ECN 8TS. All trademarks used herein are the propert of their respective owners. The use of an trademark in this tet does not vest in the author or publisher an trademark ownership rights in such trademarks, nor does the use of such trademarks impl an affiliation with or endorsement of this book b such owners. ISBN 0: -9-0-X ISBN : British Librar Cataloguing-in-Publication Data A catalogue record for this book is available from the British Librar Printed in the United States of America

3 . Studies show that teting while driving is as risk as driving with a 0.08 blood alcohol level, the standard for drunk driving. The bar graph shows the number of fatalities in the United States involving distracted driving from 00 through 008. Although the distracted categor involves such activities as talking on cellphones, conversing with passengers, and eating, eperts at the National Highwa Traffic Safet Administration claim that teting while driving is the clearest menace because it requires looking awa from the road. Number of Deaths Involving Distracted Driving Number of Highwa Fatalities in the United States Involving Distracted Driving (, ) Year Number of Deaths Involving Distracted Driving (, ) Years after 00 Source: National Highwa Traffic Safet Administration a. Shown to the right of the bar graph is a scatter plot with a line passing through two of the data points. Use the two points whose coordinates are shown b the voice balloons to write the point-slope form of an equation that models the number of highwa fatalities involving distracted driving,, in the United States ears after 00. b. Write the equation from part (a) in slope-intercept form. Use function notation. c. In 00, surves showed overwhelming public support to ban teting while driving, although at that time onl 9 states and Washington, D.C., outlawed the practice. Without additional laws that penalize teting drivers, use the linear function ou obtained from part (b) to project the number of fatalities in the United States in 0 involving distracted driving. 8. Find the average rate of change of f() = - from = 6 to = 0. - if Ú 9. If g() =, find g(-) and g(). - if 6 In Eercises 0, find the domain of each function. 0. f() = f() = If f() = - and g() =, find (f g)() and the domain of f g.. Epress h() = ( + ) as a composition of two functions f and g so that h() = (f g)().. Find the length and the midpoint of the line segment whose endpoints are (, -) and (, ). 0

4 ANSWERS TO SELECTED EXERCISES Section Check Point Eercises. domain: {0, 0, 0, 0, 0}; range: {9., 6., 0.,.,.}. a. not a function b. function. a. = 6 - ; function b. = { - ; not a function. a. b c f() ; shifted down b units. g() 6. a. function b. not a function c. function d. not a function. a. 00 b. 9 c. approimatel 0 (, ) 8. a. domain: { - } or [-, ]; range: { 0 } or [0, ] (, ) (, ) b. domain: { - 6 } or (-, ]; range: { - 6 } or [-, ) 0 (, ) c. domain: { - 6 0} or [-, 0); range: {-, -, -} (, ) (, ) (0, ) (, ) (, ) Concept and Vocabular Check. relation; domain; range. function. f;. true. false 6. ; + 6. ordered pairs 8. more than once; function 9. [0, ); domain 0. [, ); range. 0; 0; zeros. false Eercise Set. function; {,, }; {,, }. not a function; {, }; {, }. function; {,,, }; {-,, 9}. function; {-, -, -, 0}; {-, -, -, 0} 9. not a function; {}; {,, 6}. is a function of.. is a function of.. is not a function of.. is not a function of. 9. is a function of.. is a function of.. is a function of.. is a function of.. a. 9 b. + 9 c a. b c a. b. c. - + d. 8a - 9a +. a. b. c. +. a. b. c. -. a. b. - c. 9. g() (, ) f() (, ) (, ) (0, ) (, ) (, ) (, ) (, ) (, ) shifted up b units.. f() g() (, ) (, ) (, ) (, ) (0, ) (, ) (, ) (, ) (, ) shifted down b unit.. g() f() (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) shifted up b unit.. (, ) (, ) (, ) (, ) (, 0) (, ) (0, ) (, ) (, 0) g() f() shifted down b units.. f() g() (0, ) (, ) (, 6) (, 8) (, ) (, 0) (, 8) (, ) (, ) shifted up b units. 9. ( 0, ) (, ) (, ) g() f() (, ) (, ) (0, ) (, ) (, ) (, ) (, ) shifted up b units.. (, ) (9, ) (, ) f() 0 g() (0, ) (, 0) (, ) (9, ) shifted down b unit.. (, ) (9, ) (, ) f() g() 0 (0, ) (, 0) (, ) (, ) shifted to the right b unit.. function. function 9. not a function 6. function 6. function a. (-, ) b. [-, ) c. - and d. - e. f(-) = - and f() = 9. a. (-, ) b. [, ) c. none d. e. f(-) = and f() = 8. a. [0, ) b. [-, ) c. d. - e. f() = 8. a. [0, ) b. [, ) c. none d. e. f() = 8. a. [-, 6] b. [-, 6] c. d. e. f(-) = 8. a. (-, ) b. (-, -] c. none d. - e. f(-) = - and f() = a. (-, ) b. (0, ) c. none d.. e. f() = 6 9. a. {-,-, 0,, } b. {} c. none d. e. f(-) + f() = 9. -;

5 99. a. {(Philippines, ), (Spain, ), (Ital, ), (German, ), (Russia, 6)} b. es; Each countr corresponds to eactl one age. c. {(, Philippines), (, Spain), (, Ital), (, German), (6, Russia)} d. no; in the domain corresponds to two members of the range, Ital and German. 0. a. 8; The chance that a 60-ear-old will survive to age 0 is 8%. b. 6; The chance that a 60-ear-old will survive to age 0 is 6%. c. f 0. a. 8; In 00, the wage gap was 8%.; (0, 8) b. underestimates b % 0. C = 00, , where is the number of biccles produced; C(90) = 09,000; It costs $09,000 to produce 90 biccles. 0. T = 0 + 0, where is the rate on the outgoing trip; + 0 T(0) = ; It takes hours, traveling 0 mph outgoing and 60 mph returning. 9. does not make sense. does not make sense. false. false. Answers will var; an eample is {(, ), (, )}. 9. 6; For 00 calling minutes, the monthl cost is $6. 0. f(),. h + h + h (, ) (, 0) (, ) Section Check Point Eercises. increasing on (-, -), decreasing on (-, ), increasing on (, ). a. even b. odd c. neither. a. 0; With 0 calling minutes, the cost is $0.; (0, 0) b. 8; With calling minutes, the cost is $8.; (, 8). a. - - h - h + + h + b. - - h +, h 0. (, ) (, ) (, ) (, 0) if f() if Concept and Vocabular Check. 6 f( ); f( ); = f( ). maimum; minimum. -f(); origin. piecewise 6. less than or equal to ; ; -; 0. difference quotient; + h; f(); h; h 8. false 9. false Eercise Set. a. (-, ) b. (-, -) c. none. a. (0, ) b. none c. none. a. none b. (-, 6) c. none. a. (-, -) b. none c. (-, ) 9. a. (-, 0) or (., ) b. (0,.) or (, ) c. none. a. (-, ) b. none c. (-, -) or (, ). a. 0; f(0) = b. -, ; f(-) = f() = 0. a. -; f(-) = b. ; f() = -6. odd 9. neither. even. even. even. odd 9. even. odd. a. (-, ) b. [-, ) c. and d. e. (, ) f. (0, ) g. (-, 0) h. i. - j. k. and 6 l. neither. a. (-, ] b. (-, ] c. - and d. e. (-, ) f. (, ) g. (-, -] h. A relative maimum of occurs at. i. j. positive. a. - b. c a. b. c. 0. a. 8 b. c. 6. a. (, ) f() b. [0, ) (, ) if 0 if 0. a. (, ) (0, ) (, ) if 0 f() if 0 b. (-, 0] {}. a. (, ) (, ) (, 0) (, ) if f() if b. (-, ) 9. a. (, ) (, ) (, ) (, ) if if. a. (, ) (, ) (, ),. a. (, ) (, ) ( 6, 0) (, 0) f() if 0 if f() f() if 0 if if 0 b. {-, } b. [0, ) b. [0, )., h 0., h h, h h -, h h +, h h +, h h +, h h -, h 0. 0, h 0. - ( + h), h 0., h h +

6 9. 0.0t - 6 C(t) (00, ) t 0 if 0 t C(t) = (t - 00) if t 00 C(t) (0, 0) (00, 0) t 8. increasing: (, ); decreasing: (, ) 8. ears old; 8% 8. domain: [, ]; range: [, 8] 89. men 9. ; A single tapaer with taable income of $0,000 owes $. 9.,9 + 0.( -,00) ; It costs $0.8 to mail a -ounce first-class letter. 9. $ Cost Pet Insurance f() (0, ) $0 (, 0) $0 (9, 0) $0 (8, 8) (, 6) $0 (, 0) (6, ) (, ) 0 Age 0.. a. increasing: (-, ) or (, ) decreasing: (, ) b. increasing: (, ) decreasing: (-, -) constant: (-, ) increasing: (0, ) decreasing: (-, 0) c. increasing:(0, ); decreasing: (-, 0) d. f() = n is increasing for (-, ) when n is positive and odd. e.. makes sense. makes sense.. a, 0b and (0, -). = - + or = - + Section Check Point Eercises As n increases the steepness increases.. a. 6 b. -. (, ) (0, ) f() (, ) 9. f() = ; 6.6F. + = 6( - ); = = -( + ) or + 6 = -( + ); = - -. (0, ) (, ) (, ) Concept and Vocabular Check 6. (, ) (, 0) (, ). slope: - ; -intercept: (0, ) (, ) (, ) (0, ) (, 0) 6 0. scatter plot; regression -.. positive. negative. zero 6. undefined. - - = m( - ) 8. = m + b; 9. (0, ); ; 0. horizontal. vertical. general

7 Eercise Set. ; rises. ; rises. 0; horizontal. -; falls 9. undefined; vertical. - = ( - ); = -. - = 6( + ); = = -( + ); = = -( + ); = = - + ; = = ( - 0); =. + = - ( - 6); = - +. using (, ), - = ( - ); =. using (-, 0), - 0 = ( + ); = + 9. using (-, -), + = ( + ); = +. using (-, -), + = ( + ); = +. using (-, -), + = 0( + ); = -. using (, ), - = ( - ); = +. using (0, ), - = 8( - 0); = m = ; b =. m = -; b =. m = ; b = -. m = - ; b = (, ) (, ) (0, ) (, ) (0, ) (, ) f() (, ) (, ) (0, ) f() 9 (0, ) (, ). m = - ; b = 0 (, ) 9. (0, ). (, 0). 0. f() (0, ) (, ) g(). 8 0 (6, 0) 8 9. a. = - + b. m = -; b = c. (0, ) (, ) 6. a. = b. m = - ; b = 6 c. 8 (0, 6) (, ) 6. a. = - b. m = ; b = - c. (0, ) (, ) 6. a. = b. m = 0; b = c. 9 0 (0, ) (, 0) (0, 6) 69. (, 0) 6 0 (0, ). 8 (0, 6), m = - a b ; falls. undefined slope; vertical. m = - A B ; b = C B f() 6 0, 0, m, m, m, m 8. a. -. = 0.8( - 0) or = 0.8( - 0) b. f() = c..% 89. a & b. Life Epectanc for United States; E() = Males, b Year of Birth Life Epectanc c. 8.6 r (0,.) Birth Years after Answers will var; an eample is = -. +, where is the percentage of adult females who are literate and is under-five mortalit per thousand.; Predictions will var.