5. c. y (2, 5) range: [-2, ) axis of symmetry: x = 1 (0, 3) (1, 2) , 0 ( 2, 1) f(x) 2(x 2) 2 1. range: [-4, ) (0, 3) (1, 4) ( 3, 0) ( 1, 0)

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1 AA Answers to Selected Eercises CHAPTER Eercise Set.. + 6i 6. ( + i) + ( - i) = 0; ( + i)( - i) = - i = + = 0 6. (, ) (, ) Section. Check Point Eercises. f() ( ) Eercise Set.. (0, ) (, ) f() ( ). () (0, ) (, ) f() 0. (, ). ( -, ). ( -, - ). (, - ) 6. (, ). range: [-, ) ais of smmetr: = (0, ) (, ) f() ( ). (). range: [-, ) ais of smmetr: = ( ) ( ) (, ) f() ( ). (). c. Arrow's Height (feet) f() (00) (0, ) (0) Arrow's Horizontal Distance (feet). range: [, ) ais of smmetr: = (, ) f() ( ). (, ) (, ) f() g() ( ) (, ) 0. range: [, ) ais of smmetr: = 6 (0, ) (, ) 6 f() ( ). range: [, ) range: [, ) range: [-, ) range: a-, d ais of smmetr: = ais of smmetr: = ais of smmetr: = - ais of smmetr: = 6 (0) (, ) 6 (0, ) (, ) (, ), ( ). range: (-, ] ais of smmetr: = ( ) 6. range: (-, ] ais of smmetr: = f() ( ). range: [-, ) ais of smmetr: = f(). range: [-6, ) ais of smmetr: = () (, ) () (0, ) (, ) ( ) 6 () 6 (, 6) f() ( ) f() ( ) f() f(). range: c -, b ais of smmetr: = - 0. range: c -, b ais of smmetr: =. range: (-, ] ais of smmetr: =. range: (-, ] ais of smmetr: = - ( ), () (0, 0) 6 (0, ) () 6, (, ) ( ) (0, ) () f() 0 f() f() f()

2 Answers to Selected Eercises AA. range: [-6, ) ais of smmetr: = -. range: [-, ) ais of smmetr: = -. range: [-, ) ais of smmetr: = - 6. range: c -, b ais of smmetr: = 0 ( 6) 0 (, 6) ( 6) f() 6 ( ) ( ) (, ) f() 0 (, ) (0, ) f() 0 (0, ) f(),. range: (-, - ] ais of smmetr: = (0, ) (, ) f(). range: [, ) ais of smmetr: = (0, 6) (, ) f() 6. a.minimum b.minimum is - at =. c. ; range: [-, ) 0. a.minimum b.minimum is - at =. c. ; range: [-, ). a.maimum b. Maimum is at =. c. ; range: (-, ]. a.maimum b. Maimum is at = -. c. ; range: (-, ]. a.minimum b.minimum is - at =. c. ; range: c -, b. a.minimum b.minimum is - at =. c. ; range: c -, b.; range: [-, ) 6.; range: (-, -]. f() = ( + 0) -. f() = -( + ) +. f() = -( - ) -. f() = ( - ) 6. f() = ( - ). c. 60. c. f() and ; and 0; d b. d; 6. sq d. 6 f() (,.) 6. 0 d b 0 d; 00 sq d. in.; sq in.. $; $6 (.,.) 6 (0, 6) 6 (0, 6) Ball's Vertical Distance (feet) (.6) 0 0 Ball's Horizontal Distance (feet) Ball's Vertical Distance (feet) (.) Ball's Horizontal Distance (feet). a d. You can choose Xmin and Xma so the -value of the verte is in the center of the graph. Choose Ymin to include the -value of the vert. (0, 600) 00 0 You can onl see a little of the parabola (., ). ( -). ( -0, ) a & d. The greatest number of viewers actuall occurred in Season, not Season 6, and the model underestimates the greatest number b 0. million. 00. f() = ( + ) - 0. a, b 0. $; $, f() = -; f() = 6 ; The graph passes through (, -), which is below the -ais, and (, 6), which is above the -ais. Since the graph of f is continuous, it must cross the -ais somewhere between and to get from one of these points to the other.

3 AA6 Answers to Selected Eercises Section. Check Point Eercises. (, ) (, ) f() 0. 0 ( ) (, ) (0, ) (, ) (, 6) f() ( ) ( ) Eercise Set..polnomial function; degree:. polnomial function; degree:. = has multiplicit ; The graph crosses the -ais; = - has multiplicit ; The graph touches the -ais and turns around. 6. = - has multiplicit ; The graph crosses the -ais; = - has multiplicit ; The graph touches the -ais and turns around.. = has multiplicit ; The graph crosses the -ais; = -6 has multiplicit ; The graph crosses the -ais.. = - has multiplicit ; The graph crosses the -ais; = has multiplicit ; The graph crosses the -ais.. = 0 has multiplicit ; The graph crosses the -ais; = has multiplicit ; The graph touches the -ais and turns around. 0. = 0 has multiplicit ; The graph crosses the -ais; = - has multiplicit ; The graph touches the -ais and turns around.. =, = - and = - have multiplicit ; The graph crosses the -ais.. =, = -, and = - have multiplicit ; The graph crosses the -ais.. f(-) = -; f(-) =. f(-) = -; f(-) =. a. f() rises to the right and falls to the left. b. = -, =, = - ; f() crosses the -ais at each. c.the -intercept is -.. a. f() rises to the right and falls to the left. b. = -, =, = -; f() crosses the -ais at each. c.the -intercept is -. ( ) () ( ) () (0, ) (0, ) (, 6) f(). a. f() rises to the left and the right. b. = 0, =, = - ; f() crosses the -ais at - and ; f() touches the -ais at 0. c.the -intercept is 0. d. -ais smmetr 0 f(). a. f() rises to the left and the right. b. = 0, =, = -; f() touches but does not cross the -ais at 0; f() crosses the -ais at - and. c.the -intercept is 0. d. -ais smmetr ( ) (, 0) (, 0) () f(). a. f() falls to the left and the right. b. = 0, =, = - ; f() crosses the -ais at - and ; f() touches the -ais at 0. c.the -intercept is 0. d. -ais smmetr 0 (, 6) (, 6) ( ) () f() 6 f() 6. a. f() falls to the left and the right. b. = 0, =, = -; f() touches but does not cross the -ais at 0; f() crosses the -ais at - and. c.the -intercept is 0. d. -ais smmetr (, ) ( ) (, ) () f()

4 Answers to Selected Eercises AA. a. f() rises to the left and the right. b. = 0, = ; f() touches the -ais at 0 and. c.the -intercept is 0. (, ) (, ) () (0..06) f(). a. f() falls to the left and the right. b. = 0, = ; f() crosses the -ais at 0 and. c.the -intercept is 0. (, ) () f(). a. f() rises to the left and falls to the right. b. = 0, = { ; f() crosses the -ais at 0; f() touches the -ais at and -. c.the -intercept is 0. d.origin smmetr (, ) (, ) () ( ) (, ) (, ) f() 6. a. f() rises to the left and falls to the right. b. = 0, = ; f() crosses the -ais at ; f() touches the -ais at 0. c.the -intercept is 0. (, ) (, ). a. f() rises to the left and the right. b. = 0, = ; f() touches the -ais at and 0. c.the -intercept is 0. (.,.06) 0 (, ) f() 6 0. a. f() falls to the left and the right. b. = 0, = ; f() crosses the -ais at 0 and. c.the -intercept is 0. (0..) (, ) () f(). a. f() rises to the left and falls to the right. b. = 0, = { ; f() crosses the -ais at -, and. c.the -intercept is 0. d.origin smmetr () ( ) (, ) f() 6. a. f() falls to the left and the right. b. = {; f() crosses the -ais at - and. c.the -intercept is. d. -ais smmetr 0, () f(). a. f() falls to the left and the right. b. =, = -, = ; f() crosses the -ais at - and ; f() touches the -ais at. c.the -intercept is. (0, ) 0 () ( ) () f() ( ) ( ) f() 6. a. f() falls to the left and the right. b. =, = -, = ; f() crosses the -ais at - and ; f() touches the -ais at. c.the -intercept is 00. (00) 000 () (, 6) () ( ) 0 (, ) f() ( ) ( )

5 AA Answers to Selected Eercises. a. f() rises to the left and the right. b. = -, = 0, = ; f() crosses the -ais at - and ; f() touches the -ais at 0. c.the -intercept is 0. 0 (, 6) ( ) () (, ) f() ( ) ( ). a. f() falls to the left and the right. b. = -, = 0, = ; f() crosses the -ais at - and ; f() touches the -ais at 0. c.the -intercept is 0. (, ) ( ) () f() ( )( ) 6. a. f() falls to the left and the right. b. = -, = 0, = ; f() crosses the -ais at - and 0; f() touches the -ais at. c.the -intercept is ( 0) () ( ) (, ) f() ( ) ( ) 6. a. f() rises to the left and the right. b. = -, =, = ; f() crosses the -ais at - and ; f() touches the -ais at. c.the -intercept is () (, 6) ( ) (, 00) () (0, 6) f() ( ) ( ) ( ). a. f() rises to the left and the right. b. = -, = -, = 0 ; f() crosses the -ais at - and 0; f() touches the -ais at -. c.the -intercept is 0. ( ) f() ( ) ( ) 60. a. f() falls to the left and the right. b. = -, = 0, = ; f() crosses the -ais at - and ; f() touches the -ais at 0. c.the -intercept is 0. d. -ais smmetr (, ) (, ) ( ) () f() ( )( ) 6. a. f() falls to the left and the right. b. = -, = 0, = ; f() crosses the -ais at - and 0; f() touches the -ais at. c.the -intercept is 0. (, 6) ( ) 00 () (, 0) f() ( ) ( ) 6. a. f() rises to the right and falls to the left. b. = -, = -, = -; f() crosses the -ais at each. c.the -intercept is. ( ) ( ) (, ) f() ( ) ( ) ( ) 6. a. -, odd;, odd;, odd b. f() = ( + )( - )( - ) c. 66. a. -, odd;, odd;, odd b. f() = ( + )( - )( - ) c a. -, odd;, even b. f() = ( + )( - ) c. 6. a. -, odd;, even b. f() = ( + )( - ) c. 6. a. -, even;, even b. f() = -( + ) ( - ) c a. -, even;, even b. f() = -( + ) ( - ) c a. -, even; -, odd;, odd b. f() = ( + ) ( + )( - ) c. -. a. -, odd; -, even;, odd b. f() = ( + )( + ) ( - ) c. -. a. 6; The world tiger population in 00 was approimatel 6.; (0, 6) b.underestimates b c. rises to the right; no; The model indicates an increasing world tiger population that will actuall decrease without conservation efforts.. a. 6,; The world tiger population in 0 was approimatel 6,.; (0, 6,) b.underestimates b c. rises to the right; es; The model indicates an increasing world tiger population that might actuall increase with conservation efforts.. a. from through min and from through 0 min b. from through min and from 0 through min negative; The graph falls to the left and falls to the right. f. 6 { beats per min; 0 min g. 6 { beats per min; min 6. positive; The graph falls to the left and rises to the right. f. +. { +0.0; 0 g. +. { +0.0; 00

6 Answers to Selected Eercises AA Eercise Set a. 0; When the ta rate is 0%, ta revenue is $00 billion.; (0) b ; f(0) = 0; es - 0 c.no, f is a rational function because it is a quotient of two polnomials. 6. a. 6 ; When the ta rate is 0%, ta revenue is 6 tens of billions of dollars, or approimatel $6. billion.; a0, 6 b b ; f(0) 6.; es - 0 Eercise Set.. a. {, {, {, {6, {, {. c ,, and c.no; f is a rational function because it is a quotient of two polnomials.. {, {, {, {, {, {, {, {. {, {, {, {6, {, {, {, { 6. {, {, {, {, {, {, {, {. {, {, {, {, {6, {. b. -, -, or 0. a. {, {, {, {, {6, { b. -,, or b. -,, or. b ,, or. c. -,, and. c. -, - + i, and - - i 6. c., + i, and - i. a. {, {, {, {, {6, { b. -,, or. b. - or. a. {, {, {, {, {6, {. a. {, {, {, {, {, {, { 6, { 6 b. -,, or. a. {, {, {, {. a. {, {, { b. - or. a. {, {, {, { b. - or. f() = f() = f() = f() = f() = f() = f() = b. 0 ( ) (0, 6) (, 6) () () 0 (, 6) f() 6 6. b. 0 () (0, ) 0 (, ) f(). b. (0, ) 0 f() 6. b. 0 (, ) (, ) f(). b. 0 (0, 6) (, 0) f() 6. b. (0, 6) (). b. () 0 (0, ) 0 ( ) ( ) () ( ) (, 0) f() 6 f() b. (0, ) () f() 6. e -,, f.,, or positive real zeros; no negative real zeros

7 AA0 Answers to Selected Eercises real zero, nonreal comple zeros 00 0 real zeros, nonreal comple zeros.makes sense.makes sense 0.false real zeros, nonreal comple zeros Mid-Chapter Check Point. { i. (0, ) 00 real zeros, nonreal comple zeros () () (, ) f() ( ) range: [-, ). 0 (0, ) () f() ( ) ( ). (0, ) (, ) ( ) f() ( ) range: (-, ]. 0 (0, ) () f() ( ) ( ) ( ) 0. (, ) 0 (0, ) ( ) () 0 f() range: (-, ]. 6 (0, ) (, ) f() 6 range: [-, ). (0, ). (0, ) 0 ( ) () () f() ( ) () () f() 6 6. (, ) f() ( ) 6 0. () () (0, ). () f() 6. () f() f() = f() = es. 00 (, 0) () f() 6 f() Section.6 Check Point Eercises. (, ) g() Eercise Set.6. 0, () f() (, 6) (, ) 6. 0,,, 0, f()., f(). {, - }. {, -6 }. {, - } 6. {, - }.all real numbers.all real numbers.vertical asmptote: = -; no holes.vertical asmptote: = ; no holes.vertical asmptotes: = -, = 0 ; no holes.vertical asmptotes: =, = 0; no holes.vertical asmptote: = -; hole at = 0 6.vertical asmptote: = ; hole at = 0,