Chapter Functions and Graphs... ( ) ( y y ) ( 7) ( ) y y y ( 6) ( ) 6 9 5 5 6y 6y 6y9 9 ( y ) y y Solution set:. 5. a. h, k 6, r ; ( ) [ y( 6)] ( ) ( y6) ( y6) b. ( ) ( y) [ ( )] ( y) So in the standard form of the circle s equation ( h) ( yk) r, we have h, k, r. center: ( h, k) (, ) radius: r = c. domain: 5, range:, Section.9 Check Point Eercises. d y y ( ) ( ) 6 96 5 5 6.7 d 6. y y y y y y y y ( ) ( y) 9 [ ( )] ( y) So in the standard form of the circle s equation ( h) ( yk) r, we have h, k, r... 7 ( ) 8,,, h, k, r ; ( ) ( y) y 6 Copyright Pearson Education, Inc.
Section.9 Distance and Midpoint Formulas; Circles Concept and Vocabulary Check.9 5. d ( ) ( ).. ( ) ( y y ) ; y y. circle; center; radius. ( h) ( yk) r 5. general 6. ; 6 Eercise Set.9.. d ( ) (8 ) 5 5 69 d (8 5) (5 ) 96 5 5 96 5 5 6. 7. 8. d () 96 5 5 d [ ( )] [ ( 6)] 5 5 9 5.9 d [ ( )] [ ( )] 6 6 6.. d 6 ( ) 6 6 9.77. d 5 ( ) 8 96 7 8.5 9. d ( ) [ ( )] 6 6 5.66 Copyright Pearson Education, Inc. 5
Chapter Functions and Graphs. d. [ ] [] 6 5 6 5 6. d (.5.5) (6.8.) ( ) ( ) 6 5.7. d (.6.6) 5.7. 7 9 5 5 7.7 5. d ( ) ( 5 5) ( ) ( 5) 6() 9(5) 8 5 9 9.6 6. d 5 6 6 6 966 7 96.9 7. 7 6 d 5 5 ( ) 5.. d ( 5 ) [ ( )] ( 5) ( ) 5 8.8. 7 d 7 9 7 8. 9... 6 d 7 7 6 7 7. 6 8 8,, (,6) 6,, (6,5) ( 6) 8 ( ), 8, (, 5) 6 Copyright Pearson Education, Inc.
Section.9 Distance and Midpoint Formulas; Circles. 7 5,, 5, 5. 5 6 6 5,, 6,,.. 5. 6 ( 8),,, 6 8 6 5 5, 5, 7 5, 8 6,,,.. ( ) ( y) 7 y 9 ( ) ( y) 8 y 6. y 5 y 5 y( ). y 6 5. y ( ) y 6. 7 5 5 5 5, 5, 5,, 5 5 5 7. 8. 9. 8 ( 6) 5 7 5, 5,,5 5 7 6 ( ) 8,, 5, 8,,, (,) 6. y ( ) 5 y 5 9 7. ( ) y( ) y 8. ( 5) y( ) 5 y 5 5 9. y ( ) y. y ( ) 6 y 6 Copyright Pearson Education, Inc. 7
Chapter Functions and Graphs. y 6 ( ) ( y) y h, k, r ; center = (, ); radius =. y 6 ( ) ( y) h, k, r ; center = (, ); radius = domain: range:,, domain: range:,6, 7. y 9 ( ) ( y) 7 h, k, r 7; center = (, ); radius = 7 5. ( ) ( y) [ ( )] ( y) h, k, r center = (, ); radius = domain: range: 7,7 7,7. y y 6 6 h, k, r 6; center = (, ); radius = 6 domain: 5, range:, 6. y 5 ( ) ( y) 5 h, k, r 5; center = (, ); radius = 5 domain: range:, 9 5, 7 domain: range: 6,, 9 8 Copyright Pearson Education, Inc.
Section.9 Distance and Midpoint Formulas; Circles 7. ( ) ( y) [ ( )] [ y( )] h, k, r center = (, ); radius = 5. y h, k, r ; center = (,); radius = domain: range:,, domain:, range:, 8. y5 6 y ( ) ( 5) 6 h, k 5, r 6; center = (, 5); radius = 6 y 5 5. h, k, r 5; center = (,); radius = 5 domain: range:,, domain: range: 6, 5,5 9. y h, k, r ; center = (, ); radius = y 6 5. h, k, r ; center = (,); radius = domain:, range:, domain: range: 6,, Copyright Pearson Education, Inc. 9
Chapter Functions and Graphs 5. y 6y6 y y y y 6 6 6 9 96 y ( ) 9 ( ) center = (, ); radius = 56. y y9 y y 9 y y 6 6 9 y 6 9 ( ) ( y6) 7 center = (, 6); radius = 7 5. y 8y6 8 y y 6 y y 8 6 6 y y ( ) ( ) center = (, ); radius = 57. y y y y y 8y8 8 8 8 6 68 y y 5 ( ) ( ) 5 center = (, ); radius = 5 55. y 6y y y y y 6 5 6 9 5 9 y 5 6 ( 5) ( y) 8 center = (5, ); radius = 8 58. y 6y y 6y y y 6 6 9 6 9 y ( 6) 7 center = ( 6, ); radius = 7 Copyright Pearson Education, Inc.
Section.9 Distance and Midpoint Formulas; Circles 59. y 5 y y 5 5 y y 6 center = (, ); radius = 6. y y y y y y y center =, ; radius = 6. y 6y7 y 6y 7 y y 6 9 9 7 y 6 ( ) ( y) center = (, ); radius = 6. y y y y 9 9 y y 7 y center =, ; radius = 7 6. y y y y y y y center =, ; radius = Copyright Pearson Education, Inc.
Chapter Functions and Graphs 6. 9 y 5y 9 y 5y 9 5 9 9 5 y 5y 5 5 y 5 center =, ; radius = 5 66. a. Since the line segment passes through the center, the center is the midpoint of the segment. y y M, 5 6 8,,,5 The center is,5. b. The radius is the distance from the center to one of the points on the circle. Using the point, 6, we get: 5 6 d The radius is units. 65. a. Since the line segment passes through the center, the center is the midpoint of the segment. y y M, 7 9,, 5, The center is 5,. b. The radius is the distance from the center to one of the points on the circle. Using the point, 9, we get: c. 5 9 d 5 The radius is 5 units. 5 y 5 y 5 5 67. c. y5 y 5 Intersection points:, Check, : 6 Check, : and, 6 6 true true 6 6 6 true true The solution set is,,,. Copyright Pearson Education, Inc.
Section.9 Distance and Midpoint Formulas; Circles 68. 7. 69. Intersection points:, Check, : 9 and, 9 9 true true Check, : 9 9 9 true true The solution set is,,,. Intersection points:, Check, : 9 Check, : 9 9 9 true 9 9 9 9 true and, The solution set is,,, true true. Intersection points:, and, 7. d (895 ) (87 ). d 7,5,77. d 69 The distance between Boston and San Francisco is about 69 miles. Check, : 9 Check, : true true true true The solution set is,,,. 7. d (896 88) (5 65). d,79,. d 8 The distance between New Orleans and Houston is about 8 miles. 7. If we place L.A. at the origin, then we want the equation of a circle with center at.,.7 and radius.. y.7 y..7 9 7. C(, 68 + ) = (, 8) ( ) ( y8) 68 ( y8) 6 Copyright Pearson Education, Inc.
Chapter Functions and Graphs 75. 8. Answers will vary. 8. 8. 85. 9. The distance for A to B: AB () [d d ] 8 The distance from B to C: BC (6 ) [d 6 d ] 99 8 The distance for A to C: AC (6 ) [6 d ( d )] 86. makes sense 87. makes sense 88. does not make sense; Eplanations will vary. Sample eplanation: Since r this is not the equation of a circle. 89. makes sense 9. false; Changes to make the statement true will vary. A sample change is: The equation would be y 56. 9. false; Changes to make the statement true will vary. A sample change is: The center is at (, 5). 9. false; Changes to make the statement true will vary. A sample change is: This is not an equation for a circle. 9. false; Changes to make the statement true will vary. A sample change is: Since r 6 this is not the equation of a circle. 5 5 5 5 5 5 ABBC AC 5 5 5 95. a. d is distance from (, ) to midpoint y y d y d d y y y y y y y y y d d y y y y d y y y y Copyright Pearson Education, Inc.
Section. Modeling with Functions d is distance from midpoint to, y y y d y d d y y y y y y y y y d d y yy y d y yy y d d b. d is the distance from, y to y ( ) ( ) d y y d y y y y d d d because a a a 96. Both circles have center (, ). The smaller circle has radius 5 and the larger circle has radius 6. The smaller circle is inside of the larger circle. The area between them is given by π 6 π 5 6π 5π π.56square units. 97. The circle is centered at (,). The slope of the radius with endpoints (,) and (, ) is m. The line perpendicular to the radius has slope. The tangent line has slope and passes through (, ), so its equation is: y ( ). 98. 99. a. p l w () () A lw ()() The perimeter is yd; the area is sq yd. b. p l w (5) () A lw (5)() The perimeter is yd; the area is sq yd πrh h πr πr πrh πr πr πr π r r Section. Check Point Eercises. a. f() = 5 +.8 b. g() = +. c. 5 +.8 = +. =. = The plans cost the same for tet messages.. a. N() = 8 ( ) = 8 + = 8, b. R() = (8, ) = + 8,. V() = (5 )(8 ) = ( 6 + ) = 6 + Since represents the inches to be cut off, >. The smallest side is 8, so must cut less than off each side. The domain of V is or, in interval notation,,.. l + w = l = w l = w Let = width, then length = A() = ( ) = square feet Copyright Pearson Education, Inc. 5
Chapter Functions and Graphs 5. V πr h πr h h πr Ar () πr πrh πr πr πr π r r 6. I( ).7.9(5, ) 7. d ( ) y y y d 6 Concept and Vocabulary Check...5. ; 5( ); 5; 5( ). ; ; ; ; ;. y ; y; 9 ; (9 ) 5...9 y;, ;..9(, ) 6. y ; Eercise Set. 6. a. f( ).5 b..5.5 8 8 miles. a. f( ) 8.5 b. 95 8.5 5.5 86 You drove 86 miles for $95.. a. M 9.. b. 8 9... 59. 98 98 years after 95, in 5, someone will run a minute mile.. a. P ( ) 8.6 b. 8 6.6 years after 99, in, % of babies born will be out of wedlock. 5. a. f( ).5 b. g( ).5 c..5.5.75 8 f (8).5(8) 5 g(8).5(8) 5 If a person crosses the bridge 8 times the cost will be $5 for both options 6. a. f( ).5 b. g( ) c..5.5 f ().5() 5 g() 5 To cross the bridge times costs the same, $5, for either method. 6 Copyright Pearson Education, Inc.
Section. Modeling with Functions 7. a. f( ).8 b. g( ).9 c..8.9 6. 6 For $6 worth of merchandise, your cost is $58 for both plans 8. a. f( ).7 b. g( ).9 c..7.9 6. f ().7() g().9() You would have to purchase $ in merchandise at a total cost of $. 9. a. N( ), 5( ), 5, 5 b. R( ) (, 5 ) 5,. a. N( ), ( 5), 6 6, b. R( ) (6, ) 6,. a. N( ) 9 5(5 ) 9 5 75 65 5 b. R( ) (65 5 ) 5 65. a. N( ) 7, 6(9 ) 7 6 5 6 b. R( ) ( 6 ) 6. a. Y( ) ( 5) 5 b. T( ) (5 ) 5. a. Y( ) 7 ( ) 7 9 6 b. T( ) (6 ) 6 5. a. V( ) ( )( ) (576 96 ) 96 576 b. V () () 96() 576() 8 If -inch squares are cut off each corner, the volume will be 8 square inches. V () () 96() 576() 97 If -inch squares are cut off each corner, the volume will be 97 square inches. V () () 96() 576() If -inch squares are cut off each corner, the volume will be square inches. V (5) (5) 96(5) 576(5) 98 If 5-inch squares are cut off each corner, the volume will be 98 square inches. (6) (6) 96(6) 576(6) 86 V If 6-inch squares are cut off each corner, the volume will be 86 square inches. c. If is the inches to be cut off, >. Since each side is, you must cut less than inches off each end. < < Copyright Pearson Education, Inc. 7
Chapter Functions and Graphs 6. a. V( ) ( )( ) (9 ) 9 b. V () ( ) ( ) 9() 78 If inches are cut from each side, the volume will be 78 square inches. V () ( ) ( ) 9() 96 If inches are cut from each side, the volume will be 96 square inches. V (5) (5 ) (5 ) 9(5) If 5 inches are cut from each side, the volume will be square inches. V (6) (6 ) (6 ) 9(6) 9 If 6 inches are cut from each side, the volume will be 9 square inches. V (7) (7 ) (7 ) 9(7) 79 If 7 inches are cut from each side, the volume will be 79 square inches. c. Since is the number of inches to be cut from each side, >. Since each side is inches, you must cut less than 5 inches from each side. < < 5 or (, 5) 7. A( ) ( ) 8. 8 A ( ) 6 6 6 6 66 6 8 8 9. P ( ) (66 ) 66. P ( ) (5 ) 5. A( ) ( ). A( ) ( ). wl 8 l 8 w Let w A( ) (8 ) 8. wl 6 l 6 l let width, 6 length A ( ) (6 ) 6 5. y y y A ( ) ( ) 6. y y y A ( ) ( ) (6 ) (6 ) 8 Copyright Pearson Education, Inc.
Section. Modeling with Functions 7. distance around straight sides π r distance around curved sides π r π r πr Ar () ( πr)rπr rπr πr rπr 8. = distance around the straight sides πr = distance around the curved sides π r 88 88π r πr A( ) r( πr) πr rπr πr r y 9. y C ( ) 75 5,, 5 5,, 75. 5 lw 5 w; let l l 5 C ( ) 9 5 9 5 9. y y A ( ). y y. A 5 y y A( ) ( ). 8 y 8 y A (8 ) 8 5. a. Let = amount invested at 5% 5 = amount invested at 7% I() =.5 +.7(5 ) b. 6.5.7 (5 ) 6.55.7 5.8 5 5 5 875 Invest $,5 at 5% and $8,75 at 7%. Copyright Pearson Education, Inc. 9
Chapter Functions and Graphs 6. a. Let = amount at % 8,75 = amount at % I( )..(875 ) b...(875 ) 7.5. 7. 665 The amount of money to be invested should be $665 at % and $ at %. 7. Let = amount invested at % 8 = amount invested at 5% loss I() =..5(8 ) 8. Let = amount at % = amount at 6% I( )..6( ).7.6.8 7 9... d ( ) ( y) y 8 6 7 6 d ( ) ( y) y 8 6 6 5 6 d ( ) y. d ( ) y. a. A ( ) y. a. b. b. P ( ) y A ( ) y 5. 6-foot pole c 6 9 P ( ) ( ) y 6 8-foot pole c 9 8 ( ) c 6 c 6 total length f( ) 6 6 6. Road from Town A: c 6 c 6 Road from Town B: c ( ) c 9 c 5 f 6 5 Copyright Pearson Education, Inc.
Section. Modeling with Functions 7. A ( ) ( 5) ( ) ( ) ( 5) ( ) 5 A ( ) ( ) A( ) A ( ) 8. A ( ) ( ) (6 )( ) ( )( ) (8) A ( ) ( ) 86 A ( ) 86 A ( ) 6 6 9. 5. V( ) ( 5)()( ) ( 5)()( ) V( ) ( 5)( 5) ( 5) V( ) 5 7 5 V( ) V( ) ( )()( ) ( )( ) () ( ) V( ) ( )( 5) ( ) V( ) 5 V( ) 7 5. 6. Answers may vary. 6. does not make sense; Eplanations will vary. Sample eplanation: This model is not reasonable, as it suggests a per minute charge of $. 6. does not make sense; Eplanations will vary. Sample eplanation: The decrease in passengers is modeled by 6( ). 65. does not make sense; Eplanations will vary. Sample eplanation: The area of a rectangle is not solely determined by its perimeter. For eample: A by 6 rectangle and a by 7 rectangle both have perimeters of units, yet their areas are different from each other. 67. Distance and time rowed: d d rt d t t Distance and time walked: d 6 rt d 5t 6 6 t 5 Total time: 6 T( ) 5 68. A ( ) ( )( ) () 6 6 69. P h r ( π r) hrπr rπr h rπr h rπr A r πr rr πr πr rr πr 66. makes sense Copyright Pearson Education, Inc.
Chapter Functions and Graphs 7. r h. 7. V( h) πr h π h π hh π h h (7 )( 5 ) 565 95 or 5 9. =, y = 6 =, y = =, y = =, y = =, y = =, y = =, y = 6 7. 8 8 9 7. 7 5 5 8 5 5 5 5 6 5 6 =, y = =, y = =, y = =, y = =, y = =, y = =, y =. Chapter Review Eercises. =, y = 8 =, y = 6 =, y = =, y = =, y = =, y = =, y =, y, y, y, y, y, y, y Copyright Pearson Education, Inc.
Chapter Review Eercises 5. A portion of Cartesian coordinate plane with minimum -value equal to, maimum -value equal to, -scale equal to and with minimum y-value equal to 5, maimum y-value equal to 5, and y-scale equal to. 5. function domain: {,, 5} range: {7} 6. function domain: {,, } range: {, 5, π} 7. not a function domain: {, } range: {, 5, 9} 6. -intercept: ; The graph intersects the -ais at,. y-intercept: ; The graph intersects the y-ais at,. 7. -intercepts:, ; The graph intersects the -ais at, and,. y-intercept: ; The graph intercepts the y-ais at,. 8. -intercept: 5; The graph intersects the -ais at 5,. y-intercept: None; The graph does not intersect the y- ais. 9. The coordinates are (, 8). This means that 8% of college students anticipated a starting salary of $ thousand.. The starting salary that was anticipated by the greatest percentage of college students was $ thousand. % of students anticipated this salary.. The starting salary that was anticipated by the least percentage of college students was $7 thousand. % of students anticipated this salary.. Starting salaries of $5 thousand and $ thousand were anticipated by more than % of college students. % of students anticipated a starting salary of $ thousand.. p.s.8s.7 p.().8().7 p 9.7 This is greater than the estimate of the previous question. 8. y 8 y 8 Since only one value of y can be obtained for each value of, y is a function of. 9.. y y Since only one value of y can be obtained for each value of, y is a function of. y 6 y 6 y 6 Since more than one value of y can be obtained from some values of, y is not a function of.. f() = 5 7. a. f() = 5 7() = b. f( ) 57( ) 57 76 c. f( ) = 5 7( ) = 5 + 7 g ( ) 5 a. b. g() () 5() g( ) ( ) 5( ) Copyright Pearson Education, Inc.
Chapter Functions and Graphs c. d. g ( ) ( ) 5( ) ( ) 55 g( ) ( ) 5( ) 5. a. domain: (, ) b. range:, c. -intercepts: and d. y-intercept:. a. g() 9. a. b. g() = = c. g( ) = ( ) = 7 ( ) f ( ) b. f() = c. f () 5. The vertical line test shows that this is not the graph of a function. 6. The vertical line test shows that this is the graph of a function. 7. The vertical line test shows that this is the graph of a function. 8. The vertical line test shows that this is not the graph of a function. e. increasing: (, ) decreasing: (, ) f. f( ) = and f(6) =. a. domain: (, ) b. range: [, ] c. -intercept: d. y-intercept: e. increasing: (, ) constant: (, ) or (, ) f. f( 9) = and f() =. a., relative maimum b.,, relative minimum, 5 5. a., relative maimum b. none 9. The vertical line test shows that this is not the graph of a function.. The vertical line test shows that this is the graph of a function.. a. domain: [, 5) b. range: [ 5, ] c. -intercept: d. y-intercept: e. increasing: (, ) or (, 5) decreasing: (, ) or (, ) 6. f( ) 5 f( ) ( ) 5( ) 5 f( ) The function is odd. The function is symmetric with respect to the origin. f. f( ) = and f() = 5 Copyright Pearson Education, Inc.
Chapter Review Eercises 7. f( ) f( ) ( ) ( ) f( ) The function is even. The function is symmetric with respect to the y-ais.. 8( h) (8) h 88h8 h 8h 8 8 8. f( ) f( ) ( ) ( ) f( ) The function is odd. The function is symmetric with respect to the origin.. ( h) ( h) h hh h h hh h h h h h h hh h h. a. Yes, the eagle s height is a function of time since the graph passes the vertical line test. b. Decreasing: (, ) The eagle descended. 9. a. c. Constant: (, ) or (, 7) The eagle s height held steady during the first seconds and the eagle was on the ground for 5 seconds. d. Increasing: (7, ) The eagle was ascending... a. b. range: {, 5} b. range: yy 5. 6. m ; falls 5 m ( ) ; rises ( ) Copyright Pearson Education, Inc. 5
Chapter Functions and Graphs 7. m ; 6 ( ) 9 horizontal 5. slope: ; 5 y-intercept: 8. 5 5 m ( ) undefined; vertical 9. point-slope form: y = 6( + ) slope-intercept form: y = 6 6 5. 6 m point-slope form: y 6 = ( ) or y = ( + ) slope-intercept form: y = + 55. slope: ; y-intercept: 5 5. + y 9 = y = + 9 m = point-slope form: y + 7 = ( ) slope-intercept form: y = + 7 y = + 5 5. perpendicular to y m = point-slope form: y 6 = ( + ) slope-intercept form: y = 9 + 6 y = 5. Write 6 y in slope intercept form. 6 y y 6 y 6 The slope of the perpendicular line is 6, thus the slope of the desired line is m. 6 y y m( ) y( ) 6 ( ) y ( ) 6 y 6 6y6 6y8 56. y6 y 6 y slope: ; y-intercept: 57. y 8 y 8 y slope: ; y-intercept: 6 Copyright Pearson Education, Inc.
Chapter Review Eercises 58. 5y Find -intercept: 5() 5 Find y-intercept: () 5y 5y 5y y 6. a. d. f( ).6.56 f ().6().56.7. According to the function, France has about. deaths per, persons. This underestimates the value in the graph by.7 deaths per, persons. The line passes below the point for France. 5 6 m.8 985 5 b. For each year from 985 through, the percentage of U.S. college freshmen rating their emotional health high or above average decreased by.8. The rate of change was.8% per year. 59. 5 6. 6. a. f( ) f( ) [9 9 ] [ 5] 95 S() 6() 6() 8 8 S() 6() 6() 8 8 b. S() 6() 6() 8 8 6. a.. 8.7 m.6 9 5 75 y y m( ) y.69 or y..6 5 b. y.69 y.6. y.6.56 f( ).6.56 c. According to the graph, France has about 5 deaths per, persons. 6. 8 c. The ball is traveling up until seconds, then it starts to come down. Copyright Pearson Education, Inc. 7
Chapter Functions and Graphs 65. 7. 66. 7. 67. 7. 68. 7. 69. 75. 7. 76. 8 Copyright Pearson Education, Inc.
Chapter Review Eercises 77. 8. 78. 8. 79. 85. domain: (, ) 86. The denominator is zero when = 7. The domain is,7 7,. 8. 8. 8. 87. The epressions under each radical must not be negative. 8 8 domain: (, ]. 88. The denominator is zero when = 7 or =., 7 7,, domain: 89. The epressions under each radical must not be negative. The denominator is zero when = 5.,5 5, domain: 9. The epressions under each radical must not be negative. and 5 5 domain:, Copyright Pearson Education, Inc. 9
Chapter Functions and Graphs 9. f() = ; g() = 5 (f + g)() = 6 domain: (, ) (f g)() = ( ) ( 5) = + domain: (, ) 9. ( fg)( ) ( )( 5) 6 5 domain: (, ) f ( ) g 5,5 5, domain: f( ) ; g( ) ( f g)( ) domain: (, ) ( f g)( ) ( ) ( ) domain: (, ) ( fg)( ) ( )( ) f ( ) g domain:,,, 9. f( ) 7; g( ) ( f g)( ) 7 domain: [, ) ( f g)( ) 7 domain: [, ) ( fg)( ) 7 5 domain: [, ) f 7 ( ) g domain: (, ) 9. f( ) ; g( ) a. b. c. ( f g)( ) () 6 8 ( g f)( ) ( ) ( f g)() 6() 8() 95. f( ) ; g() = + 96. a. a. ( f g)( ) b. ( g f)( ) c. ( f g)() f g f b.,,, 97. a. f g f( ) b. [, ) 98. f( ) g( ) 99. f g( ) 7 5 Copyright Pearson Education, Inc.
Chapter Review Eercises 5. f( ) ; g( ) 5 5 f( g( )) 5 6 5 7 5 g( f( )) 5 5 6 7 6 f and g are not inverses of each other.. f( ) 5 ; g( ) 5 f( g( )) 5 5 ( ) (5 ) 5 g( f( )) 5 5 f and g are inverses of each other.. a. f( ) y y y f ( ) b. f( f ( )) () f ( f( )). a.. a. f( ) 8 y 8 8y 8y y 8 y 8 y f ( ) b. f f f ( ) 8 8 8 8 f( ) 8 f( ) 5 y 5 5 y y 5y y 5y y ( 5) y 5 f ( ) 5 Copyright Pearson Education, Inc. 5
Chapter Functions and Graphs b. f f f ( ) 5 5 ( 5) 5 55 f( ) 55 5. The inverse function eists. 6. The inverse function does not eist since it does not pass the horizontal line test. 7. The inverse function eists. 8. The inverse function does not eist since it does not pass the horizontal line test. 9.. f( ) y y y ( ) y. f ( ) ( ), d [ ( )] [9 ( )] 5 5 69. d [ ( )] 5 8.8. f( ) y y. 5. 6,, 5,5 ( 5) 6,,, y y f ( ) 6. 7. y y 9 ( ( )) ( y) 6 ( ) ( y) 6 5 Copyright Pearson Education, Inc.
Chapter Review Eercises 8. center: (, ); radius:. a. f( ) 5.5 b. g( ) 5.7 domain: range:,, 9. center: (, ); radius: c. 5.5 5.7. 5 For 5 minutes, the two plans cost the same.. a. N( ) ( ) 6 b. R( ) (6 ) 6 domain: 5, range:,6. y y y y y y ( ) ( y) 9 center: (, ); radius:. a. w6 l V( ) (6 )( ) b. < < 8 5. lw l w w l Let width w A ( ) ( w) domain: range:, 5, 6. V lwh 8 h 8 h. a. W( ) 567 5 b. 7 567 5 5 5 9 9 years after, in 9, the average weekly sales will be $7. A ( ) h 8 7. I =.8 +.(, ) Copyright Pearson Education, Inc. 5
Chapter Functions and Graphs Chapter Test i.. (b), (c), and (d) are not functions.. a. f() f( ) = ( ) = 5 b. domain: ( 5, 6] c. range: [, 5] d. increasing: (, ). j. f( ) f( ) ( ) e. decreasing: ( 5, ) or (, 6) f., f() = 5 g. (, ) h. -intercepts:,, and 5. i. y-intercept:. a., b., c. d. even; f( ) f( ) e. no; f fails the horizontal line test f. f () is a relative minimum. g. 5. 6. domain:, range:, domain: range:,, domain:, range: {} h. 5 Copyright Pearson Education, Inc.
Chapter Test 7.. 8. domain:, range:,. domain of f:, range of f:, domain of g:, range of g:, 9. domain: range: 5,, domain of f:, range of f:, domain of g:, range of g:,.. domain:, range:, domain of f:, range of f:, domain of f :, range of f :, domain: range: 6,, 7 Copyright Pearson Education, Inc. 55
Chapter Functions and Graphs. 5. 6. 7. domain of f:, range of f:, domain of f :, range of f :, domain of f:, range of f:, domain of f :, range of f :, f( ) f( ) ( ) ( ) f( h) f( ) h ( h) ( h) h hh h h h h h h hh h h 8. ( g f )( ) 6 9. 6 f ( ) g 6,, domain:. ( f g)( ) f g( ). ( g f )( ) g f( ) (6) (6) 66 68 6 86... 5. g f( ) ( ) ( ) 6 6 6 6 f( ) f( ) ( ) ( ) f is neither even nor odd. m 8 9 point-slope form: y = ( ) or y + 8 = ( + ) slope-intercept form: y = 5 y 5 so m = point-slope form: y 6 = ( + ) slope-intercept form: y = + 56 Copyright Pearson Education, Inc.
Chapter Test 6. Write y5 in slope intercept form. y5 y 5 y 5 The slope of the parallel line is, thus the slope of the desired line is m. y y m( ) y( ) ( 7) y ( 7) y y 7. a. 587 57 99 Find slope: m point-slope form: y y m y57 8. b. slope-intercept form: y57 y57 y 8 f( ) 8 c. f( ) 8 () 8 868 According to the model, 868 fatalities will involve distracted driving in. () 5 [(6) 5] 6 5 9 8 9. g( ) = ( ) = g(7) 7. The denominator is zero when = or = 5., 5 5,, domain:. The epressions under each radical must not be negative. 5 and 5 domain:,. 7 7 ( f g)( ), domain:,,, 7.. f g d ( ) ( y y ) d ( ) y y (5 ) ( ) 96 5 5 y y 5,, 7, The length is 5 and the midpoint is 7, or.5,. 5. a. T( ).78.9 b. 5.7.78.9 6.8.9 years after 98, in, the winning time will be 5.7 seconds. Copyright Pearson Education, Inc. 57
Chapter Functions and Graphs 6. a. Y( ) 5.5( ) 5.5 5 95.5 b. T( ) (95.5 ).5 95 7. lw 6 l 6w l w Let w A( ) ( ) 8. V lwh 8 h 8 h 8 A ( ), 58 Copyright Pearson Education, Inc.