CHAPTER 7. Think & Discuss (p. 399) x is curved and not a. x 0. straight line r r 3. 6 cm r. Skill Review (p.

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1 CHAPTER Think & Discuss (p. 99). (, 8) because the graph is curved and not a straight line. about kg; locate mm on the graph and read the curve at the point directl above mm. Skill Review (p. ) Estimated weight 9 abc a b c 8 (8, ) (, ) (, ) Femur circumference 8 9. Guided Practice (p. ). n is the inde of the radical na (the nth root of a).. a. Alwas true; take the nth root of each side of the first equation to get the second equation. b. Sometimes true; if a then. ; no real rth root; When n is even, there are onl nth roots for nonnegative numbers n n r r cm r 9 r.8. Practice and Applications (pp. ) ± none ±. ±.. ± , , ± ±. ± ± ± ± or ±.. Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

2 .. Mongoose Camel Horse Swiss cow.. V.a. v.8a.a n where n is odd q clh q.9 q. ft sec,8 s b l r a. b. 8 ±..8a.9 a 9. a.8 ft a A.9s.9s s V ml V 9,.9 ml V,9. ml V,. ml V r V, in. r. cm a r. r. in. r c. V. V 9,, in. d.,.% 9,, e. The fraction is cut in half;.8% 9. a < a a > n is even no real n is odd. Real roots eist whenever the line a crosses the graph. This happens twice for a >, once for a, not at all for a <.. i p n p i 9, 9 i.8. Mied Review (p. )..... A 8 8 A det A A 9 9 A a a > a a < 8 det det det 9 det Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

3 . 8. ; product of powers propert 9. power of a power and negative eponent properties 8. power of a power, power of a product, and ; negative eponent properties 8. negative eponents and zero eponents properties ; 8. ; quotient of powers propert 8. negative eponents and power of a quotient ; properties 8. quotient of powers propert ; 8. ; product of powers and quotient of powers properties A ; f 9 8,,, f 9 9,,, f 8 i i, i, i f i i i, i, Copright McDougal Littell Inc. det Lesson.. Guided Practice (p. ). Sample answer:, ;, ; 9, 8.,, 9. ; to add or subtract like radicals, use the Distributive Propert. ; use the power of a power propert ± ± a a.. b b b b 8. 8 z z z z 9. a a a a.. S km cm. Practice and Applications (pp. ) , , Algebra Chapter Worked-out Solution Ke

4 r. 9. S.8. r ,.9 cm. 9. d z z z z z z z z z z z z.. 9 z z z zz z 8z Algebra Chapter Worked-out Solution Ke 9. lowest; highest; f 9. f. Higher notes have frequencies twice as high as lower notes of the same letter. d v v g g S.9.. mm f.8 f 9. v v g v g 9. V S V V V 98. a. S cm V...8. cm Yes, the surface area is large enough. b. S 8,,, 9, cm V 8,, cm No, the surface area is not large enough. c. S rh r V r h rh r r h; Surface Area increased b a factor of,,; Volume increased b a factor of,,,; Giant ants don t eist because their volume increases times as fast as their surface areas, so the could not meet their ogen needs. 99. Absolute value of is needed if m is odd and n is even. Copright McDougal Littell Inc.

5 . Mied Review (p. ).9. c 9. c.. c c c 9. 8 c ) 8 8 ) ) 8 ) Quiz (p. ) P,9. about, horsepower S. 9,8.m S.m.8 Lesson... Guided Practice (p. 8) ±.. power function; real; rational. Sometimes; the sum is a power if the eponents (b) are the same.. The equation is g f.. f 9 ; The entire quantit is squared.. ;. ; all real numbers all real numbers. ; 8. all real numbers ; all real numbers ecept 9. ;. ; all real numbers all real numbers. g f ; The bonus is. times the amount over $,,, so calculate the amount first and then take %.. Practice and Applications (pp. 8 ) ±.9. 8 ; all real numbers Copright McDougal Littell Inc. Algebra 9 Chapter Worked-out Solution Ke

6 . 8 ; all real. ; all real numbers numbers ; 9 all positive real numbers all ; real numbers.. 8; ; all real numbers but all real numbers. 8 ; all real 8. f numbers ;. 8 ; all real numbers all real numbers ecept 8. f f ; all real numbers 9. g ; 9. g g ;. ; all real numbers all real numbers nonnegative real numbers. f ; all real numbers. ;. ;. g ; all real nonnegative real numbers all real numbers numbers. 9;. ;. m m m. 9 m ; nonnegative real numbers positive real numbers Multipling beats per minute b number of minutes per. lifetime gives us the number of beats per lifetime.. ; all real numbers ;. rw.w. w. positive real numbers ecept.w. ; all real numbers ecept r f r,,. 8 ; r,,. positive real numbers g ; positive real numbers. f ; all real numbers ecept.. g 9 nonnegative real numbers. ; all real numbers. 9 ; all real numbers. ; all real numbers. all real numbers ecept ;. f ; all real numbers. g ; all real numbers 8. f ; all real numbers 9. g 8; all real numbers. ; all real numbers. ; all nonnegative real numbers. ; all real numbers. 8; all real numbers. ; all real numbers. Sample answer: % off of $ is $. rather than $.. There is a smaller discount after the subtraction... For addition and subtraction, combine like terms. For multiplication and division, use the distributive propert and properties of eponents. For composition of functions f g, enter the function g as in the function f. 8. f g f 8 88; f g f.; A 9. g f g ; g f g ; B..9 $. h.9.f cm f f f ; f f f 8,,; A. gg g. 8.8; gg g ; B. h ; Sample answer: f ; g. h ; Sample answer: f, g. h Sample answer: f, g ; Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

7 . h ; Sample answer: f ; 8. 9 g. h 9; Sample answer: f, ±. g h ; Sample answer: f, g 8. Mied Review (p. ) or a b c 8 b c a c a b 8. A Lesson A CO NG RA TU LA TI ON S_ Developing Concepts Activit. (p. ) g. The reflect one another.. g is a function that multiplies b then adds.. f g ; gf 8. 8., Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

8 Developing Concepts Activit. (p. ) Eploring the Concept. a. ;. The graphs of a relation and its inverse are reflections of one another in the line.. Switch and in the original equation and solve for... g. Graph the reflection.. g is the function that subtracts from and then divides b. Both compositions equal. Since both compositions equal, then the functions are inverses. Drawing Conclusions.b. g. Graph the reflection.. g is the function that multiplies b and then adds. Both compositions equal. Since both compositions equal, the functions are inverses.. c. ; ; g f g8 8 f g ; gf.. f g f 8 8 ; 8 9. No. Horizontal lines such as cross the graph more than once.. Practice and Applications (pp. 8) g. Graph the reflections.. g is the function that subtracts from and then multiplies b. Both compositions equal, and therefore are inverse of one another.. Guided Practice (p. ). If no horizontal line crosses the graph of the function more than once, then the inverse relations is an inverse function. Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

9 f g f g f g f g f g f g f g f g. A. C. B f f Yes, the inverse is a function. Yes, the inverse is a function. Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

10 . f. f 9. No, the inverse is not No, the inverse is not a function. a function.. f. f Yes, the inverse is a function... Yes, the inverse is a function. No, the inverse is not No, the inverse is not a function. a function.. f 9. D C.D us 8. f No, the inverse is not a function. C 9F 9 C F F 9 F 9 F f....d C D us.... f ; B. f ; f A 9 h a f f w 8.9 d w 8.9 d d 8.9 w f f f.8 h.9 a 9 h a 9 w 9. l w 9. l.9.9 cm 9. d 8.9. in. w 9. l f 9 9 f 9 9 f 9 f f f. Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

11 . f and f are their own inverses because. f. the are their own reflections. f.. 8. ; a, where a is a real number. Mied Review (p.9) f 9.. f.. f f. f. f Quiz (p. 9). ; nonnegative real numbers. ; nonnegative real numbers. ; nonnegative real numbers. all positive real numbers ;. f 8 all real numbers ecept 8 8 ;. g all real ecept 8;. f all real numbers ecept ; 8. g ; all real numbers 9.. b a. p b a. p b.8 A b det A 8 8 $. f g f 9 9 g Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

12 . 8.. f. 8 8 f.. f No, the inverse does not pass the vertical line test. No, the inverse does not pass the vertical line test.. f 8. f. f. No, the inverse is not a function. f Yes, the inverse passes the vertical line test. 9. f... Yes, the inverse passes the vertical line test. f No, the inverse is not a function. Yes, the inverse is a function.. Art A.t.t.t A t.t A.. ft Yes, the inverse passes the vertical line test.... f No, the inverse does not pass the vertical line test. f 8 Technolog Activit. (p. ). f. f. No, the inverse does not pass the vertical line test. No, the inverse does not pass the vertical line test. Yes, the inverse passes the vertical line test. Yes, the inverse passes the vertical line test. Lesson. Activit. (p. ). f.. f.. a. b. (, ) (, ) (, ) (,.) Yes, the inverse passes the vertical line test. No, the inverse does not pass the vertical line test. Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

13 c. d (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ). a. b.,.., (, ) (, ) (, ) (,.) (, ) (,.) (, ) (, ) (,.8) (, ) (, ) (, ) c. d. (, ) (, ) (, ) (, ) (, ) (, ), are all real numbers.. (, ) (, ) (, ), are all real numbers (, ) (, ) (8, ) In Step and Step the absolute value of a determines how much the graph a is stretched or compressed compared with the graph of. The sign of a determines whether there is a reflection in the -ais. The variable a affects the graph of a in a similar fashion as compared with the graph of.. Guided Practice (p. ). radical. The coordinates have been switched. The should be, and,.. The coordinates given do not solve the equation. The should be,,,, and,.. Shift the graph of f left units.. Shift the graph of f down units... (, ) (, ) (, ) (, ), are all real numbers. about. ears, are all real numbers. Practice and Applications (pp. ). Shift the function left units.. Shift the function right units and units down.. Shift the function down units. 8. Shift the function left units and down units. 9. B. A. C.. (, ) (, ) (, ) (,.),,,, Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

14 .... (,.) (,.) (, ) (, ) (,.) (,.) (,.) (, ) (, ) (, ),,.... (, ) (, ) (8, ) (, ) (.,.) (,.) (.,.9) (, ) (,.8) (,.),, (, 9) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (,.). Sample answer:,. Sample answer:,,,. Sample answer:,... Sample answer:, are all real numbers.. Sample answer:, are all real numbers. (, ) (,.8) (,.) (, ) (, ). Sample answer:, are all real numbers.. about.9 ft Distance (miles) 8,.. (, ) (, ) (,.) (8, 9) (, 8) (8, ). about.... Radius... 8 Altitude (feet above sea level) Surface area 8 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

15 8. about horsepower Speed (miles per hour) 9. about 8. nautical miles Speed (knots). a. The graphs are reflections across the -ais. b. g c Power (horse power) 9 Fetch (nautical miles) f The graphs are reflections across the -ais. f (, ) (, ) f g g (9, 9) d. To graph radical functions of the form f a h k or g a h k. sketch a or a.. reflect graph across -ais.. shift the graph h units horizontall and k units verticall.... (, ) (, ). Mied Review (p. ) ± 9 9 ± ± g f g f ( g f g. a. c i b. c i c. c z z i ± f 8 z 9 i z i z z i z i z 9 i ± 8 ± ±..... ± no no es ± z z z z Copright McDougal Littell Inc. Algebra 9 Chapter Worked-out Solution Ke

16 Lesson.. Guided Practice (p. ). An etraneous solution is a solution to an equation raised to a power that is not a solution to the original equation.. Net, she will have to take the square root of both sides. To solve the equation in one step, she could have raised both sides to the power.. First, he should have rewritten the equation with onl one radical epression on each side: , does not work in original equation; no solution..9s s.. s.. s.. s;. mihr. Practice and Applications (pp. ) es no es es no es ,, Solution does not solve original equation, therefore there is no solution Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

17 The square root of an number will never be negative, 8 8 therefore there is no solution Two positive numbers 89. never add up to zero. no solution , ,9 no solution 9, Copright McDougal Littell Inc.,8. Algebra Chapter Worked-out Solution Ke

18 ... d.... t sec. 9.8 d.9 Cannot take the th root of a negative number; no solution. 99 h 9.. In this case, is a d. m h h solution to the equation, but 8 is an etraneous solution..9 h.. E 8 8 t t. in. d.8t 9.t d d.8.8t 9.t. 9.8t 9.t. t.9s s.. s. 8. s..8 s.8 C. mm C 9.8 d. d.8, E B. C , 9. no solution Mied Review (p. ) Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

19 intercept: 8. -intercept:.9 local min.:.,. local min.: none local ma.:, local ma.: none intercepts: ± 89. -intercept:, ±. local min.:, local min.:.9,.8 local ma.: none local ma.:.9,.8 9. C Math and Histor (p. ). d.. Lesson.. Guided Practice (p. 9). The mean is the average. It is calculated b dividing the sum of the numbers b n, the number of numbers. The median is the middle number when the numbers are written in ascending order. If n is even, the median is the mean of the two middle numbers. The mode is the number or numbers that occur most frequentl. The range is the difference between the greatest and least data values.. Sample answers:,,, ;,,, 9; second set. The first set has greater range because >.. mean range Cost of printing announcements ($). d.8 d.9 km d median 8 mode Number of announcements 9. d.9 d 8. distance time rate 9. kmh. 9. Number of scores Interval Tall Frequenc Scores. Practice and Applications (pp. 9 ). mean 8.; median 9; mode 9. mean 9.; median ; mode. mean ; median 8.; mode 9. mean 8.; median ; mode. mean 9..; median.9; mode.9. mean. 9.; median.; mode,.. range ; 8.. range 9 8; range ; range 9 ; 8, range...;. range.8..; Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

20 .. Interval Tall Frequenc Frequenc Values Interval Tall Frequenc. Interval Tall Frequenc Frequenc 8 Values Interval Tall Frequenc Frequenc 8 Frequenc Values Values 9 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

21 . Frequenc Interval Tall Frequenc Values. Machine : mean..9; median.9; mode none Machine : mean mode none.9; median.9;. Machine : range...;. Machine : range..9.;.99. Machine is more consistent because it has a smaller range and standard deviation.. mean,, $,.; median,; mode none. range,,9 $,; $, The highest selling price makes the mean price higher than si out of the seven of the home prices. Reporting the median rather than the mean eliminates the huge effect of one outling value. 9. The mode is the most appropriate measure because it would indicate that most people have a positive opinion on the issue. Because the categories are not part of an order scale, means and medians are not meaningful.. Presidents ;.. Sample answer: The range of ages of Vice-Presidents is greater than the range of ages of Presidents.. ;. Number of Presidents Number of games Age Pres. V.P Ages 8 AFC margin of victor Points AFC NFC Number of Vice Presidents. Sample answer: You cannot conclude that one conference has a larger margin of victor than the other.. Answers ma var.. B 8. B 9. C 8 8 Number of games Vice Presidents Ages NFC margin of victor Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

22 .. Mied Review (p. ) f. f (, ). f. (, ) (, ) (,.9 ) (, ) (, ) f (, ) (, ) (, ) (, ) (, ) (, ). f 9. Quiz (p. )... (8, ) 8 (, ) (, ). 8., all real numbers (, ) (, 9) (, ) (,.) (, ) f (, ) (, ) (, ) (, ).. 8. mean. median. mode range (, ) (, ) Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

23 8. mean.8 9. r Chapter Review (pp. 8) median. ± 8 mode none. range v 9 cubic units Volume a.. 8 ± 8. a a Statehood Radius States Year ± 8 Technolog Activit. (p. ). mean. median. range 8.. The restaurant in the eercise has a lower mean and median fat content and a lower standard deviation than the restaurant in the eample. Overall the second restaurant has sandwiches with less fat than the first restaurant.. Answers ma var.. The second has sandwiches with a lower fat content. The bo-and-whisker plots make it clear where the median and ranges are, so it is clear that the second restaurant s sandwiches have less fat.. The second restaurant s sandwiches have fewer calories on average than the other restaurant z z z a a 8a a a a f g f g 9. f g 8 8 f. g. f g f 8... Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

24 ... and are all ; real numbers g. f f g g f ; mean 9.9 median mode (, ) (, ) (,.) range 8 (, ) (, ) 8.8. (, ) (, ) (, ) (, ) (,.) and are all real numbers Chapter Test (p. 9)..... ±.. 8. z 9 z f g 8 8 f g f g 9 8. Frequenc f g.. f g f g f g. f 8. f Values 9. f. f 8 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

25 . f. f. Actresses Actors (,.) 8 (, ) (, ) (, ) ; and are all real numbers. f. f and are all real numbers no solution (, ) (, ) (, ).. mm. Best Actress Best Actor 8 mean 9 median: 8 (, ) mode:,, 9 range: mean 8 9 median: ; mode:,, range: 9 (, ) (, ) (, ).. Best Actress Best Actor. Sample answer: Best actresses are usuall between and ears old while best actors are between ears old. Chapter Standardized Test (p. ). ± C. 8 8 A. z z z D. h f g 8 C. f B Interval Freq. 8 Interval Freq. 8 Frequenc Frequenc 8 8 Actresses Age Actors 8 8 Age Copright McDougal Littell Inc. Algebra 9 Chapter Worked-out Solution Ke

26 . f. C C E. B. C. f 8 8 f C. f f f f f f B. a. b. c. 9, k9 k 9.9 s 9.9 m B s kcalkg 9 d. s kcalkg. e. Sample Answer: Specific metabolic rate increases as bod mass decreases because the rate is proportional to m. In other words, as mass increases, the denominator gets bigger so the rate gets smaller.. a. f w w 9.9w b. wp.p c. d f wp.9p d. th f cm th f cm th f cm The distance traveled per pedal rotation increases as gear numbers increase. Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.