Sections 5.1, 5.2, 5.3, 8.1,8.6 & 8.7 Practice for the Exam

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1 Sections.1,.2,.3, 8.1,8.6 & 8.7 Practice for the Eam MAC 1 -- Sulivan 8th Ed Name: Date: Class/Section: State whether the function is a polnomial function or not. If it is, give its degree. If it is not, tell wh not. 1) f() = A) Yes; degree 4 B) Yes; degree 2 C) Yes; degree 3 D) Yes; degree 1 1) 2) f() = 1-4 A) Yes; degree 1 B) No; is a negative term C) No; it is a ratio D) Yes; degree 2) 3) f() = 3/2 - + A) Yes; degree B) Yes; degree 3/2 C) No; is raised to non-integer 3/2 power D) Yes; degree 3 3) 4) 9( - 1)12( + 1) A) Yes; degree 9 B) Yes; degree 17 C) Yes; degree 12 D) Yes; degree 8 4) For the polnomial, list each real zero and its multiplicit. Determine whether the graph crosses or touches the -ais at each -intercept. ) f() = 3( + 6)( + )4 ) A) -6, multiplicit 1, touches -ais; -, multiplicit 4, crosses -ais B) 6, multiplicit 1, touches -ais;, multiplicit 4, crosses -ais C) 6, multiplicit 1, crosses -ais;, multiplicit 4, touches -ais D) -6, multiplicit 1, crosses -ais; -, multiplicit 4, touches -ais 6) f() = 2(2 + 2)( + 6)2 A) -6, multiplicit 2, crosses -ais B) -2, multiplicit 1, crosses -ais; -6, multiplicit 2, touches -ais C) -2, multiplicit 1, touches -ais; -6, multiplicit 2, crosses -ais D) -6, multiplicit 2, touches -ais 6) 7) f() = 1 4 4(2-3) 7) A) 0, multiplicit 4, touches -ais; B) 0, multiplicit 4, crosses -ais; 3, multiplicit 1, crosses -ais; 3, multiplicit 1, touches -ais; - 3, multiplicit 1, crosses -ais - 3, multiplicit 1, touches -ais C) 0, multiplicit 4, crosses -ais D) 0, multiplicit 4, touches -ais 1

2 Solve the problem. 8) Which of the following polnomial functions might have the graph shown in the illustration below? 8) A) f() = 2( - 2)2( - 1)2 B) f() = ( - 2)( - 1)2 C) f() = 2( - 2)( - 1) D) f() = ( - 2)2( - 1) Find the - and -intercepts of f. 9) f() = 9-3 A) -intercepts: 0, 3, -3; -intercept: 9 B) -intercepts: 0, 3, -3; -intercept: 0 C) -intercepts: 0, -9; -intercept: 0 D) -intercepts: 0, -9; -intercept: 9 9) Find the power function that the graph of f resembles for large values of. ) f() = ( + 7)( + 8)3 A) = 8 B) = C) = 3 D) = 1 ) Determine the maimum number of turning points of f. 11) f() = -2( + 3)3(2-1) A) 7 B) C) 2 D) 6 11) Use the -intercepts to find the intervals on which the graph of f is above and below the -ais. 12) f() = (- 4)2( + )2 A) above the -ais: (-, -),(4, ) B) above the -ais: (-, 4) below the -ais: (-, 4) below the -ais: (-, -),(4, ) C) above the -ais: no intervals D) above the -ais: (-, -),(-, 4), (4, ) below the -ais: (-, -),(-, 4), (4, ) below the -ais: no intervals 12) 2

3 Analze the graph of the given function f as follows: (a) Determine the end behavior: find the power function that the graph of f resembles for large values of. (b) Find the - and -intercepts of the graph. (c) Determine whether the graph crosses or touches the -ais at each -intercept. (d) Graph f using a graphing utilit. (e) Use the graph to determine the local maima and local minima, if an eist. Round turning points to two decimal places. (f) Use the information obtained in (a) - (e) to draw a complete graph of f b hand. Label all intercepts and turning points. (g) Find the domain of f. Use the graph to find the range of f. (h) Use the graph to determine where f is increasing and where f is decreasing. 13) f() = ( + 3)( - 1)2 13) 14) f() = -2( - 1)( + 3) 14) Find the - and -intercepts of f. 1) f() = ( + 3)( - 2)( + 2) A) -intercepts: -2, 2, 3; -intercept: -12 B) -intercepts: -3, -2, 2; -intercept: -12 C) -intercepts: -3, -2, 2; -intercept: 12 D) -intercepts: -2, 2, 3; -intercept: 12 1) Analze the graph of the given function f as follows: a) Find the - and -intercepts of the graph of f. Round to two decimal places, if necessar. b) Determine whether the graph crosses or touches the -ais at each -intercept. c) End behavior: find the power function that the graph of f resembles for large values of. d) Use a graphing utilit to graph the function. Approimate the local maima rounded to two decimal places, if necessar. Approimate the local minima rounded to two decimal places, if necessar. e) Determine the number of turning points on the graph. f) Put all the information together, and connect the points with a smooth, continuous curve to obtain the graph of f. 16) f() = ( - 2)3( - 3)2( - 4) 16) - - Find the domain of the rational function. 17) R() = A) { -2, 2, -3} B) { -2, 2} C) { 0, 4} D) all real numbers 17) 3

4 18) G() = 3-27 A) { 9} B) { -3, 3} C) { 3} D) { -3} ) Q() = A) { -6, 6, -8} B) { -6, 6} C) { 0, -36} D) all real numbers 18) 19) Use the graph to determine the domain and range of the function. 20) 20) A) domain: { 3} range: { 4} C) domain: { 4} range: { -3} B) domain: { 4} range: { 3} D) domain: { -3} range: { 4} 21) 21) A) domain: { 0} range: { -6 or 6} C) domain: all real numbers range: { -6 or 6} B) domain: { -6 or 6} range: { 0} D) domain: { 0} range: all real numbers 4

5 Find the vertical asmptotes of the rational function. 7 22) F() = + 9 A) = -9 B) = 7 C) = 9 D) none 22) 23) Q() = A) = -1, = 1 B) = -1, = -7 C) = -1, = 1, = -7 D) none ) R() = A) = - 22 B) = -11, = 2, = -3 C) = -11, = 2 D) = 11, = -2 23) 24) Give the equation of the horizontal asmptote, if an, of the function. 2) G() = A) = 2 B) = 0 C) = 1 D) none 2) 26) F() = A) = 1 B) = 4 C) = 2 D) none 26) 27) T() = ) A) = 9 8 B) = 8 3 C) = 0 D) none ( - 1) 28) G() = A) = 0, = -2 B) = 1 C) = 0 D) none 28) Find the indicated intercept(s) of the graph of the function. 7 29) -intercept of f() = A) 0, 7 23 B) 0, C) (0, 7) D) none 29) 30) -intercept of f() = A) (0, 1) B) (0, 8) C) (0, -3) D) none 30)

6 - 6 31) -intercepts of f() = A) (-6, 0) B) (6, 0) C) (3, 0) D) none (- 9)(2 + 9) 32) -intercepts of f() = ) 32) A) (-9, 0), 9 2, 0 B) (9, 0), - 9, 0 C) (9, 0), (-9, 0) D) none 2 Graph the function. 2 33) f() = ) A) B) C) D)

7 34) f() = ( + 2)( - 2) 34) A) B) C) D)

8 3) f() = 2-9 3) A) B) C) D) Verif that the values of the variables listed are solutions of the sstem of equations. 36) + = -2 - = 6 36) = -2, = -4 A) solution B) not a solution 8

9 Solve the sstem of equations b substitution. 37) + 6 = 6-8 = -8 A) = 1, = 0; (1, 0) B) = 1, = 1; (1, 1) C) = 0, = 1; (0, 1) D) = 0, = 0; (0, 0) 37) 38) - 2 = = 3 A) = 2, = 8; (2, 8) B) = 2, = 9; (2, 9) C) = 3, = 9; (3, 9) D) = 3, = 8; (3, 8) 38) Solve the sstem of equations b elimination. 39) 3 + = = 44 A) = -18, = 3; ( -18, 3) B) = -18, = ; (-18, ) C) = -, = 18; (-, 18) D) = 18, = -; (18, -) 39) Find the domain of the rational function ) G() = A) { -7, 7, -6} B) { -7, 7} C) { 0, -49} D) all real numbers 40) Solve the sstem of equations b elimination. 41) 3 - = = -24 A) = -4, = 0; (-4, 0) B) = 0, = 4; (0, 4) C) = 0, = -4;(0, -4) D) = 4, = 0; (4, 0) 41) 9

10 The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the sstems of equations. Are the points of intersection solutions to the sstem of equations (Y/N)? 42) 42) (-4, 17) (1, 2) = -1 = -3 + A) No B) Yes Solve the sstem of equations using substitution. 43) = 13 + = A) = 3, = -2; = 2, = -3 or (3,-2),(2, -3) C) = 3, = 2; = 2, = 3 or (3, 2), (2, 3) B) = -3, = -2; = -2, = -3 or (-3,-2), (-2,-3) D) = -3, = 2; = -2, = 3 or (-3, 2), (-2, 3) 43) 44) = 90 + = -19 A) = -9, = ; = -, = 9 or (-9, ), (-, 9) C) = 9, = ; =, = 9 or (9, ), (, 9) B) = -9, = -; = -, = -9 or (-9,-),(-,-9) D) = 9, = -; =, = -9 or (9,-),(,-9) 44) Solve using elimination. 4) = = 40 A) = 7, = 3; = 3, = 7; = -7, = -3; = -3, = -7 or (7, 3), (3, -7), (-7, -3), (-3, -7) B) = 7, = -3; = 7, = 3 or (7, -3), (7, 3) C) = 7, = 3; = -7, = 3; = 7, = -3; = -7, = -3 or (7, 3), (-7, 3), (7, -3), (-7, -3) D) = -7, = -3; = -3, = -7 or (-7, -3), (-3, -7) 4)

11 46) 46) = = -6 A) = 2, = 3; = 2, = -3; = -2, = 3; = -2, = -3 or (2, 3), (2, -3), (-2, 3), (-2, -3) B) = 1, = 3; = -1, = -3 or (1, 3), (-1, -3) C) = 2, = -3; = -2, = 3 or (2, -3), (-2, 3) D) = 1, = 3; = 1, = -3; = -1, = 3; = -1, = -3 or (1, 3), (1, -3), (-2, 3), (-2, -3) Graph the inequalit. 47) + < - 47) - - A) B) C) D)

12 48) ) A) B) C) D) Graph the solution set of the sstem of inequalities or indicate that the sstem has no solution. 12

13 49) > ) - - A) B) C) D)

14 0) ) A) B) C) D) Solve the sstem of equations. If the sstem has no solution, sa that it is inconsistent. 1) - 4 = = -17 A) = 2, = 3; (2, 3) B) = 4, = 2; (4, 2) C) = 2, = 4; (2, 4) D) inconsistent 1) 14

15 Answer Ke Testname: PRACTICE FOR AND 8 1) B 2) D 3) C 4) B ) D 6) D 7) A 8) B 9) B ) A 11) D 12) D 13) (a) For large values of, the graph of f() will resemble the graph of = 3. (b) -intercept: (0, 3), -intercepts: (1, 0) and (-3, 0) (c) The graph of f crosses the -ais at (-3, 0) and touches the -ais at (1, 0). (e) Local minimum at (1, 0); Local maimum at (-1.67, 9.48) (f) (-1.67, 9.48) (0, 3) (-3, 0) (1, 0) (g) Domain of f: all real numbers; range of f: all real numbers (h) f is increasing on (-, -1.67) and (1, ); f is decreasing on (9.48, 1) 1

16 Answer Ke Testname: PRACTICE FOR AND 8 14) (a) For large values of, the graph of f() will resemble the graph of = -4. (b) -intercept: (0, 0), -intercepts: (-3, 0), (0, 0), and (1, 0) (c) The graph of f crosses the -ais at (1, 0) and (-3, 0) and touches the -ais at (0, 0). (e) Local maima at (-2.19, 12.39) and (0.69, 0.); Local minimum at (0, 0) (f) (-2.19, 12.39) (-3, 0) (0, 0) (0.69, 0.) (1, 0) (2.12, -4.06) (g) Domain of f: all real numbers; range of f: (-, 12.39] (h) f is increasing on (-, -2.19) and (0, 0.69); f is decreasing on (-2.19, 0) and (0.69, ) 1) B 16) a) The -intercepts are 2, 3, and 4. The -intercept is 288. b) The graph crosses the -ais at 2 and 4, and touches it at 3. c) The graph resembles f() = 6 for large values of. d) Maimum at (3, 0); minima at (2.7, -0.0) and (3.77, -0.76) e) The graph has 3 turning points. f) - 17) B 18) C 19) C 20) A 21) A 22) A 23) D - 16

17 Answer Ke Testname: PRACTICE FOR AND 8 24) C 2) D 26) A 27) B 28) C 29) B 30) C 31) B 32) B 33) B 34) D 3) A 36) B 37) C 38) D 39) D 40) D 41) A 42) B 43) C 44) B 4) C 46) A 47) A 48) C 49) D 0) C 1) D 17