CHAPTER 2 Think & Discuss (p. 65) Skill Review (p. 66) Lesson Guided Practice (p. 71) Algebra 2

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1 CHAPTER Think & Discuss (p. 6). Enrollment tends to increase throughout the period.. Estimate the growth trend with a line, and use the line to predict future enrollment.. Skill Review (p. 66) < < < 9 > 6 7 > < Lesson.. Guided Practice (p. 7). The domain is the set of input values and the range is the set of output values.. Sample answer: A relation is not a function if an input values map to more than a single output value. If this is the case, the vertical line at that input value will contain more than one point of a graph.. Sample answer: First, construct a table of values for the equation. Then plot enough of these points that a pattern can be seen. Then connect the points with a line or a curve.. domain:,,,,, range:,, function 8. 6 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

2 Chapter continued 9... no es.. Input Output f. f g h 9 j domain: t 8 range: g 6 8. Gasoline (gal) t 6 8 g 6 8 Gasoline Remaining g t 6 t t t 7 h Time (h) f 9 no 6. Input Output 7. Input Output no no es 8. Yes; no; Sample answer: A function is alwas a relation, but a relation is not alwas a function. An set of ordered pairs is a relation, but onl those sets that do not map the same input value to more than one output value are functions. 9. Sample answer: If a relation is a function, then no vertical line intersects the graph of the relation at more than one point. If no vertical line intersects the graph of the relation at more than one point, then the relation is a function.. no. es. no. maps to each input value to a single output value namel, while matches the input value to infinitel man output values... Practice and Applications (pp. 7 7) 9. domain:,,, 6 range:,. domain:,,, range:,,,. domain:,, range:,,, Copright McDougal Littell Inc. Algebra 7 Chapter Worked-out Solution Ke

3 Chapter continued linear; f 7. linear;. not linear; 6. not linear; 7. not linear; f linear; f6 6 f f f 9. V ; the volume of a cube with sides of length units. V the volume of a sphere with ; radius units. No; Sample answer: Not ever age corresponds to eactl one place. For eample, there were -ear-olds with finishes of first and third.. Yes; Sample answer: Each Congress number corresponds to one number of Independents. 8 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

4 Chapter continued. domain:,, 6,,, range:,,,, 6, 9. No; Sample answer: The input value 6 is mapped to different output values, and.. domain: d range: p 6. Shots made Pressure (lb/in. ) p p lbin. 7. domain: 7 8 c range: 6 8 s 8 Size Pressure Versus Depth p 7 6 (,.9) (, ) 8 d s Jazz Shooting Shots attempted d 6 78 p 9 Depth (ft) Cap Size 8 (, 8) 6. ( ) 7 8, c Circumference (in.) 7 6 c s c 9. C 6. B 6. A 6. C 6. c c in. Input Output A BC Letters to digits is a function, since each letter is mapped to a single digit. Digits to letters is not a function, since each digit corresponds to three or four different letters. Mied Review (p. 7) D EF G HI J K L M N O P Q R S T U V W XY Z 8 9 Input Output A BC D EF G HI J K L M N O P Q R S T U V W XY Z Copright McDougal Littell Inc. Algebra 9 Chapter Worked-out Solution Ke

5 Chapter continued 76. no es es Lesson.. Guided Practice (p. 79). Sample answer: The slope is a measure of the rate of change of with respect to. The slope is positive if increases as increases, and is negative if decreases as increases. This corresponds to the definition of slope (change in )/(change in ).. horizontal; vertical. The are parallel if their slopes are equal; the are perpendicular if their slopes are negative reciprocals.. m. ; rises 6. m falls 9 6 ; 7. m 8 falls 6 ; 8. m horizontal 7 ; m ; rises < 8 < < 7 m 8 m 7 m < < es 79. > es undefined; vertical m 6 ; Line is steeper. Line is steeper. ; 7 m m parallel 7 ; 8..7 < or > 6.9 es 6 > 8 > <.7 m 8 8 >.... m 7 9 m neither 6 6; m m 6 7 ; m 9 6 perpendicular m 6 parallel 6 9 ; 6. distance km time 6 hr rate distance time. Practice and Applications (p. 79 8) 7. Use points, and,. m 8. Use points, and,. m km 6 hr kmh 9. Use points, and,. m undefined ;. m falls 7 ;. m 6 ; rises. m falls 7 ;. 6 m rises 6 ;. m horizontal 7 ;. m 6 6 falls 6 6 ; 6. m rises 8 ; 7. m 8 6 undefined; vertical 9 9 ; 8. m 6 rises ; Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

6 Chapter continued. m falls ;. m 8 9 undefined; vertical ;. b. c. d. a 6. If a line is horizontal, onl the values will be different; the -values will remain the same. If a line is vertical, onl the values will be different; the -values will remain the same. undefined. ; 7. m Line is steeper. Line is steeper. 8 m Line is steeper. 6 8 ; Line is steeper. ; parallel 7. m undefined ;. m m 6 8 m m m m ; m m m 8 m m m 7 9. m falls ;. m ; 8 ; perpendicular 8 9 ; perpendicular 6 ; 8 m ; neither 6. m 7. m 8. m. 9. m Yes; each slanted half of the roof rises feet of its 6 feet of the apartment building s width, which gives it a slope of 6, the same as the required b the building code. ft..6 ftear; This is the ratio of the, ears number of vertical feet the volcano must grow to the length of time it will take to grow that high... No; no; the onl possible difference is the ease of calculation with the same selections over others. Check lines and points. A good response will show calculations for at least pairs of points.. a. 8 ft. 7. b F 7F hr 8 6 6F hr ft c. d. Sample answer: The steeper the ramp, the shorter it will be. If regulation requires more run for the amount of rise, the ramp must get longer as it did from answers (b) to (c) above. 7 k k k 7 k k k 6 k k k 6 k k k 6; ; 6 6 ; F F 7 hr h ;. Mied Review (p. 8) dollars h m sec in. ear 8. ft k k k 6 k 6k 6 k k k 9 k 9 k 6k k 9. additive inverse propert 6. associative propert of addition 6. distributive propert 6. multiplicative inverse propert Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

7 Chapter continued Guided Practice (p. 86) 8. The slope-intercept form of the equation is m b, where m is the slope and b is the -intercept of the graph 6 8 of the line. The standard form of the equation of a line is 6 A B C. 8. Slope-intercept technique; the equation is in slope-intercept 67. form or or 6 6 or 6 6 or 6 6 or or or. $.8 9 $.7 $.7 9 $. 8 or or about $./oz or or 6 or. Standard form technique; the equation is in standard form and the intercepts are easil found.. m ; b. ; b intercept -intercept 8. -intercept 9. -intercept -intercept.. m ; 6 -intercept.. Lesson. Developing Concepts Activit (p. 8). Points on graph Equation of equation Slope -intercept,,,,,, 7,,,,,,, 7,, The coefficient of is the slope of its graph.. The constant term of the equation is the -intercept of its graph.. Practice and Applications (pp ) 6. B 7. A 8. C Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

8 Chapter continued (, ) (, ) (, ) (, 6).... (, 8) (, ) (, ) (, )... (, ) (8, ). (, ) (, ) (, ) (, ) (, ) (, ) (, ) 9. (, 6) (, ) (, ) (, ). m 6; b. m 9; b... m ; b. m ; b. m ; b 7 6. m ; b 7 7. B 8. C 9. A Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

9 Chapter continued w Wash-and-waes Car Washes (, 88 ) s 7 m Washes (, ) 6 w Cost of Color Advertisement The slope, 7, represents the price of each line in the ad, C while the C-intercept,, 7 represents the initial cost of 6 (6, 6) placing the colored ad. 6. Taes collected (billions of dollars) Cost (dollars) (, ) 6 7 n Area of rain forests (million hectares) Annual Ta Revenue a 6 (8,.8) 8 6 (, 88) t Time since 98 (ears) Lines Land Area Covered b Rain Forests A 8 (, (, 8.) t Time since 99 (ears) Sample answer: 67. million hectares in ; 7. million hectares in ;. million hectares in 6..s 6a 7; Sample answer: 6 student tickets, adult; 88 student, 8 adult; student, adult. 6. To find the -intercept, set equal to zero in the equation, and solve for. To find the -intercept, set equal to zero and solve for. horizontal; vertical 6. B 66. B 67. Time b motor (min) Adult m Ticket Sales a 6 (, 66 ) 8 (8, ) Mied Review (p. 88) Island Trip (, 7) Time b sail (min) 69. < < > 7. > > > Student (, ) s s Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

10 Chapter continued 7. < < <.7 or 7 or f8 8 9 f f f m 9 8. m m undefined ; Quiz (page 89). domain:,,,, range:, function. domain:,,,, range:,,, function.. 6. f 9 6 m 8 m pages 6 minutes pages minute hour hour Let T the total number of pages read in h hours. 8 h f f 9 9 m 7 6 T h h 8 8 hours minutes 8 7 m 8 perpendicular f 7 m domain:,,, range:,,, not a function 7. m m 6 8 neither 68 mi 68 mi 68 mi. 8.6mi/h 7 P.M. 8 A.M. h 7 8 h 6 h Math and Histor (p. 89). da 9 h h. 8.7mih h. d.7t d distance in miles t time in hours domain: t 8.7 range: d. Distance from NYC (mi) Titanic Voage d (, ) (8, ) Time (hours) Technolog Activit. (p. 9).... t Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

11 Chapter continued Lesson.. Guided Practice (p. 9). The constant of variation is the common value of when and show direct variation.. Given the slope, m, and the -intercept, b, use the equation m b. Given the slope, m, and a point on the line,,, use the equation m. Given two points on the line, use the points to find the slope of the line and then use the slope and one of the points to find the equation, as above.. Sample answer: the cost of a bag of apples and the weight of the fruit in the bag m m The slope needs to be undefined which means the line is horizontal; therefore m 6 m m m m perpendicular m, 6 7. m 9 6. c.p c. c 6. million cassettes. Practice and Applications (pp. 9 98) Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

12 Chapter continued b b b The equation is, the same as in Eample. The slope-intercept equation of a line is unique. m This is the same equation as in Eample, since the slope-intercept equation of a line is unique es; 7. es; a.8m A w 67. no 68. no 69. a. b. 7. P 6,t,8, P 6,,8, P,89, a.8 a $. V 9 C V 9 6 V V 66 msec min t A 7. in. A. in. c. a is the -intercept, b is the -intercept. e. 8.6t h t C.6t 8 m b m b m b m b 6. no 8. es; d. f. s.69t 7. s s $. billion h 7 l. 7 l 8. ft l r t.7 in. in. sec t 66 sec t min t Copright McDougal Littell Inc. Algebra 7 Chapter Worked-out Solution Ke

13 Chapter continued. Mied Review (p. 98) or 7 or 6 or 9 9 or 7 or or or or.. or or or or 6 9. or 8 or or or or m m 79. m 8. m m 8. m 9 9. Developing Concepts Activit. (p. 99) Good responses to the steps and 6 eercises should include all of these: a complete table with different data points an accurate scatter plot of the data a reasonable guess of the best-fitting line correct calculation of slope and -intercept, with a correct equation correct use of model to predict for cm an actual measurement to check prediction m m undefined ; 8. m Lesson.. Guided Practice (p. ). Positive correlation occurs if -tends to increase as - increases. A negative correlation occurs if tends to decrease as increases. Relativel no correlation occurs if the points show no linear pattern.. Sample answer: A positive correlation; taller men tend to have larger feet.. Sample answer: Two data points lie on the line and all the rest are above the line. There should be about as man data points below the line as there are above. 8 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

14 Chapter continued. A positive correlation; the -values tend to increase as the -values increase m FM radio stations 6 (, 97) (6, 7) (, 7) (, 78) (, 9) (, 69) (, 9). Sample answer: List the data points so that the values of are in increasing order. If the -values mostl increase along with the -values, there is a positive correlation. If the -values decrease as the -values increase, there is a negative correlation. Otherwise, there is relativel no correlation. 6 Sample answers are given Years since 989 Sample answer: Points, 7 and, about 88 stations. Practice and Applications (pp. ) 8. negative correlation 9. positive correlation. relativel no correlation positive correlation.. negative correlation relativel no correlation negative correlation. High Altitude Temperatures. Temperature ( F) 6,,, Elevation (ft) negative correlation Interval (min) Old Faithful Eruptions I d Duration (min) positive correlation Copright McDougal Littell Inc. Algebra 9 Chapter Worked-out Solution Ke

15 Chapter continued. Enrollment Years since 989 t 9. Sample answer: One possibilit would be the wa the price of a gallon of gas varies over time, since the fluctuations in the price are so erratic and cannot be predicted. Another possibilit would be the sales of some new technolog that showed up on the scene and then died out ver quickl when it was replaced b something else.. Mied Review (p. 6) a. t 88 about 9 people Life epectanc (ears) about 9 ears b. Sets sold (thousands) negative correlation Sets sold (thousands) Birth ear Black-and-White TV Sales ,, 8,,, 9 6 Color TV Sales positive correlation Year Year c. Negativel correlated; as sales of color TVs increased, the sales of black-and-white TVs decreased... 7 < < < < 6 8 < or 6 < or m 6 m 6 7 ; Line is steeper. m 7 m ; Line is steeper. Line is steeper m 6 m Line is steeper. m m 6 9 ; 9 7 ; Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

16 Chapter continued.. Lesson.6 Activit (p. 8). and. R B B B B Quiz (p. 6).. 7. relativel no correlation 6. negative correlation 7. positive correlation Height (cm) Heights of Children h t Age (ears) d.h..h ft h Technolog Activit. (page 7) m m h 6.6t 7. R R R R R B B B. The blue dots lie on or above the line; the red dots are below the line.. Sample answer: Graph the related line, solid if the inequalit is or ; dashed if the inequalit is < or >. Test a point not on the line to see if it is a solution of the inequalit and find out which region of the plane to shade..6 Guided Practice (p. ) R R B B R R R B R R R R. Sample answer: The graph of a linear equation is a line in the plane, while the graph of a linear inequalit is a half-plane with a line as its boundar.. Dashed; solid; Sample answer: The points for which A B C are solutions of the latter inequalit and are included as part of the graph b using a solid line, but are not solutions of A B < C.,. False;, so is not a solution of the inequalit.. True; for points, on. the line,. For points, below the line, the inequalit is satisfied, since the values are smaller Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

17 Chapter continued China (min) 7 6 Calls for $ (, 66 ) (., ) United States (min) One possible solution is to spend minutes on calls to China and 78 minutes on calls in the United States, for a total cost of $9.98. Another solution would be to spend minutes on calls within the United States and 6 minutes on calls to China; this uses eactl $. A third solution is minutes on calls within the United States and minutes on calls to China. This solution uses a total of $9.7.. B. C 6. A Practice and Applications (p. ). no es 6. < 9 7 es 8 < 9 7 no. 6 7 no 7 es es 9. no C. A. B Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

18 Chapter continued... 7t f Blood Pressure Readings m 8c Cheese (milligrams) 96m 8.m 7.e Evening shows c m Milk (milligrams) e (, ) 96m Movies ( 9, ) Matinee shows m.77 cups 6 m <.9 Arm (mm Hg) 9. Sample answer: You can attend matinees and no evening showings for a total of $., of each for a total cost of $ or evening showings at a cost of $.. Ankle (mm Hg) Field goals. Sample answer: 9 touchdowns and no field goals for 6 points; touchdowns and field goal for 8 points; touchdowns and field goals for points; touchdowns and field goals for 6 points; 6 touchdowns and field goal for points.. a. b. Football Scoring f (, ) 6 8 (9, ) 6 8 t c m Cost (dollars) c m Cost (dollars) d. Sample answer: c m Cost (dollars) c 7 6 c 7 6 Touchdowns Truck Rental 8 Distance driven (mi) Truck Rental 8 Distance driven (mi) Truck Rental c 7 Other companies 6 M compan 8 m Distance driven (mi) m m c. Sample answer: If I charge a lower flat rate and not the per mile charge, I will alwas be lower in price than m competitors with the same mile rate. e. Sample answer: If I raise m flat rate m total cost would be more epensive until both cars have gone a distance that would make m total cost lower Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

19 Chapter continued. Sample answer: I used the and intercepts to find two points on the line. From there I used the point-slope formula to find the equation of the line. Since the line is drawn in full and the area shaded is less than 6, the equation is written Sample answer: is the number of grams of carbohdrates and protein and is the number of grams of fat in a food that has 6 or fewer cal., or if is the number of minutes spent walking at mi/h and is the number of minutes spent riding a bike at 9 mi/h, then 9 6 represents those combinations of, that correspond to 6 or fewer miles..6 Mied Review (p. ) domain: l range: w Lesson.7.7 Guided Practice (p. 7). Piecewise functions are represented b a combination of equations. Step functions have a graphic representation that looks like a set of steps; Piecewise: Step function:. The point is included; the point is not included.. False; Sample answer: The separate pieces are graphs of different functions. The graphs don t have to be connected. For eample, a step function is a piecewise function, but the steps of its graph are not connected.. True; in substituting,, into the greatest integer function, the graphical representation is the same as the earlier step function Weeks earlier or later Bloom Times w (, ) (, ) 7 9 f, if, if > if <, if < f,, if <, if < f f f f (, ). Latitude (N). f 6, if < 6, if 8 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

20 Chapter continued. f, if <. Parking Rates. 6, if. < 8 9, if <., if. < 9 6, if <. 8, if. <.7 Practice and Applications (pp. 7 ). f. f 9. f f 9 7. h h 9. h6. h (, ) (, ) (, 9 ) 9.. (, ) Cost (dollars) (, ) Time (hours) (9, ) (, ) (, ). Sample answer: The function graphs each -value to the smallest integer that is not less than it, giving a sort of upper limit to the -values in each interval. Sample answer: The function maps each -value to the integer it rounds to.. Sample answer: The graph would not change, since the two parts of the piecewise function both give f.. Sample answer: Each open circle on the graph would be replaced b a closed circle and each closed circle b an open circle, since a < sign does not include the endpoint and goes with an open circle, while a sign does include the endpoint and goes with a closed circle f, if < or, if or >, if < f, if <, if < 6 f 9, if <, if, if < or f, if or < <, if > or, if f, if < <, if if <, if <. f,, if <, if <, if < Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

21 Chapter continued... copies cost $., which is more than the cost of copies.. c 7,.8, if < if >. Charges.. Cost (dollars) C 8 6 (, ) (, 87) (, 8) Shirts f.6, if < < 7,6., if 7, domain: < 8; range: $.7, $.7, $8., $., $.. Making Photocopies C Cost (dollars) Number of Copies Cost (dollars) Net-Da Mail C Weight (oz) 7. $ in. 6. A 6. B 6. FICA ta (dollars) t, if t d t t, if < t 8 t 6, if 8 t 9 Depth of snow (in.) Snowfall During a Storm d(t) (9, ) (8, ) 8 6 (, ) t t d 6 d, if d < d, if < d < 9 7.d, if 9 d Maimum dive time (min) Social Securit Ta ƒ() 6 (7.6,.) Income (thousands of dollars) Time (hours) Scuba Diving t(d) (, ) 7 7 (, 66 ) (, ) (9, ) 6 d Depth (ft) 6 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

22 Chapter continued.7 Mied Review (p. ) or 9 6 or 7 8 or or or or or or 9 9 or 9 6 or or 8 9 Technolog Activit.7 (p. ).. f 6.. f. 6. f 7 f or 9 or 6 or 6 or 6 6 or 6 or 7 or Lesson.8 Activit.8 (p. ). f 6 f It affects the steepness of the ras, and whether the graph is above or below the -ais;,. relativel no correlation. A non-zero value of h causes a horizontal shift in the graph; h,. 7. n T. n.. in. negative correlation. A non-zero value of k causes a vertical shift in the graph;, k. Copright McDougal Littell Inc. Algebra 7 Chapter Worked-out Solution Ke

23 Chapter continued.8 Guided Practice (p. ) the verte of the graph. If a is positive, it opens up; if a is negative, it opens down. If a <, the graph is wider than If the graph has the same shape as that of. a,. If a > the graph is narrower.. The verte should be at,, not,. The general form of the equation for an absolute value graph is a h k and so h... 7, ; opens up; narrower.., 9; opens up; same width, ; opens up; wider 6. 7., ; opens up; same width 8. 9., ; opens up; same width, ; opens up; same width 8, ; opens down; same width.., ; opens up; wider.., ; opens down; same width 9, ; opens down; narrower.. 6, ; opens up; narrower 7. domain: 7 ;, ; opens down; same width (., ) 6., ; opens up; same width 6 or 6 6, ; opens down; wider range: (, ) (7, ).7 Practice and Applications (p. ). B. C. A. C 6. A 7. B 8 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

24 Chapter continued singles 9 or or or or 7 7 or 7 Weekl sales (thousands of $). Rainstorm Log. h; hour into the storm Rate of rainfall (in./h) Music Single Sales (, ) t r..... Time (weeks) (.,.)..... Time (hours) t.... or. 6.or or 9..8or.8. Orchestra Directions. after measures and s 9 again after 6 measures. Sound level (decibels) Measure m ; es or C. D.. Copright McDougal Littell Inc. Algebra 9 Chapter Worked-out Solution Ke

25 Chapter continued Sample answer: but a b for all values of a and b. For eample a 6 b 9 6, but ab a b,.8 Mied Review (page 8) f 7 6. f ( ).87.6 Quiz (p. 8) p.d Drinks f,., Cost (dollars) Snacks d (, ) 8 6 (6, ) 6 8 p Boes of popcorn if < if > ; Rental Charges ƒ (, ) Distance (mi) f. $.. Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

26 Chapter continued Chapter Review (pp. ) es 6 6. m. 6 9 es. m 6. m ; m undefined Chapter Test (p. ) es no.. f f 7 7. f 8 Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

27 Chapter continued m m (, ) (, ).. m. about.97 misec 7. The scatter plot shows a positive correlation, which means as the number of ears since 98 increased, the number of patents issued tended to increase. Standardized Chapter Test (pp. ). C. f ; C. m 9 7 ; E. -intercept:. D 6. E -intercept: C 7. C 9. E. f 6 ; A. D. B. A Patents issued (thousands) p 6 p.t U.S. Patents Years since 98. a. 8 rows 9 rows b. rows rows c. p g d. g g 6 g rows m h m 66 m in. t m m A Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

28 Chapter continued. a. Nurse Numbers b. positive correlation c. Sample answer: n 8.t 7 d. Nurses per, people n Time (ears since 99) n about 77 nurses per, people 6. a.. 6. b c d. 6., t Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke