3/2/2017 MATH 105 Exam 2 MATH 105 Exam 2 40 Unanswered Please be sure to save at least once every 15 minutes. If you leave this page without saving, or if your session times out, any answers you have not saved will be lost. The Submit for Grading button will become available once you've answered all questions. Exams are not timed you do not have to finish an exam in one sitting as long as you have saved your answers. Q1. Determine algebraically whether f(x) = 1/x2 is even, odd, or neither. a. even b. odd c. neither Q2. Determine the slope and yintercept of the function F(x) = x/4. a. m = 0 b = 1/4 b. m = 1/4 b = 0 c. m = 4 b =0 d. m = 1/4 b = 0 Q3. The graph of a function f is given. Find the numbers, if any, at which f has a local minimum. What are the local minima? https://www.umtweb.edu/SRM/CE.aspx?d=E2D8034C803A44A6CB9BBD50984E0EF0D7ACF02EB8070CAD07C0220C3102F1B866B949A10EC50778 1/11 3/2/2017 MATH 105 Exam 2 a. f has a local minimum at x = 2 the local minimum is 0 b. f has a local minimum at x = 0 the local minimum is 3 c. f has a local minimum at x = 2 and 2 the local minimum is 0 d. f has no local minimum Q4. The graph of a function f is given. Find the numbers, if any, at which f has a local maximum. What are the local maxima? a. f has no local maximum b. f has a local maximum at the local maximum is 1 c. f has a local maximum at x = 0 the local maximum is 1 d. f has a local maximum at x = and the local maximum is 1 Q5. Determine where the function f(x) = x2 + 8x 7 is increasing and where it is decreasing. a. increasing on (4, ) and decreasing on (, 4) https://www.umtweb.edu/SRM/CE.aspx?d=E2D8034C803A44A6CB9BBD50984E0EF0D7ACF02EB8070CAD07C0220C3102F1B866B949A10EC50778 2/11 3/2/2017 MATH 105 Exam 2 b. increasing on (, 4) and decreasing on (4, ) c. increasing on (9, ) and decreasing on (, 9) d. increasing on (, 9) and decreasing on (9, ) Q6. In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.90 as soon as you get in the taxi, to which a charge of $1.70 per mile is added. Find an equation that can be used to determine the cost, C(x), of an xmile taxi ride. a. C(x) = 1.70 + 2.90x b. C(x) = 3.10x c. C(x) = 4.60x d. C(x) = 2.90 + 1.70x Q7. Find the domain of the function f(x) = 7 x. a. {x|x 7} b. {x|x 7} c. {x|x 7} d. {x|x 7} Q8. Find the average rate of change for the function f(x) = 3/(x 2) from the values 4 to 7. a. 7 b. 1/3 c. 3/10 d. 2 Q9. Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.90. The total cost to regrind 50 platens is $400. Find the linear cost function to regrind platens. If reground platens sell for $8.80 each, how many must be reground and sold to break even? a. C(x) = 1.90x + 305 45 platens b. C(x) = 1.90x + 400 38 platens c. C(x) = 1.90x + 400 58 platens d. C(x) = 1.90x + 305 29 platens Q10. For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. a. Absolute maximum: f(4) = 7 Absolute minimum: f(1) = 2 https://www.umtweb.edu/SRM/CE.aspx?d=E2D8034C803A44A6CB9BBD50984E0EF0D7ACF02EB8070CAD07C0220C3102F1B866B949A10EC50778 3/11 3/2/2017 MATH 105 Exam 2 b. Absolute maximum: f(4) = 7 Absolute minimum: none c. Absolute maximum: none Absolute minimum: none d. Absolute maximum: none Absolute minimum: f(1) = 2 Q11. The owner of a video store has determined that the profits P of the store are approximately given by P(x) = x2 + 150x + 50, where x is the number of videos rented daily. Find the maximum profit to the nearest dollar. a. $5675 b. $11,250 c. $5625 d. $11,300 Q12. The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the interval (6, 2.5). a. increasing b. decreasing c. constant Q13. Determine, without graphing, whether the quadratic function f(x) = x2 + 2x 6 has a maximum value or a minimum value and then find that value. a. minimum 7 b. minimum 1 c. maximum 1 d. maximum 7 Q14. Graph the function h(x) = 2x + 3. State whether it is increasing, decreasing, or constant. https://www.umtweb.edu/SRM/CE.aspx?d=E2D8034C803A44A6CB9BBD50984E0EF0D7ACF02EB8070CAD07C0220C3102F1B866B949A10EC50778 4/11 3/2/2017 MATH 105 Exam 2 a. b. https://www.umtweb.edu/SRM/CE.aspx?d=E2D8034C803A44A6CB9BBD50984E0EF0D7ACF02EB8070CAD07C0220C3102F1B866B949A10EC50778 5/11 3/2/2017 MATH 105 Exam 2 c. d. Q15. The graph of a function is given. Decide whether it is even, odd, or neither. https://www.umtweb.edu/SRM/CE.aspx?d=E2D8034C803A44A6CB9BBD50984E0EF0D7ACF02EB8070CAD07C0220C3102F1B866B949A10EC50778 6/11 3/2/2017 MATH 105 Exam 2 a. even b. odd c. neither Q16. Match the graph to one of the listed functions. a. f(x) = x2 8 b. f(x) = x2 8x c. f(x) = x2 8x d. f(x) = x2 8 Q17. Determine whether the relation represents a function. If it is a function, state the domain and range. {(4, 17), (3, 10), (0, 1), (3, 10), (5, 26)} a. It is a function domain: {17, 10, 1, 26} range: {4, 3, 0, 3, 5} b. It is a function domain: {4, 3, 0, 3, 5} range: {17, 10, 1, 26} c. It is NOT a function. Q18. Find (f g)(4) when f(x) = 5x2 + 6 and g(x) = x + 2. a. 80 https://www.umtweb.edu/SRM/CE.aspx?d=E2D8034C803A44A6CB9BBD50984E0EF0D7ACF02EB8070CAD07C0220C3102F1B866B949A10EC50778 7/11 3/2/2017 MATH 105 Exam 2 b. 88 c. 84 d. 90 Q19. Use the graph to find the intervals on which it is increasing, decreasing, or constant. a. Increasing on (3, 2) and (2, 4) decreasing on (1, 1) constant on (2, 1) and (1, 2) b. Decreasing on (3, 2) and (2, 4) increasing on (1, 1) constant on (2, 1) and (1, 2) c. Decreasing on (3, 2) and (2, 4) increasing on (1, 1) d. Decreasing on (3, 1) and (1, 4) increasing on (2, 1) Q20. Find the average rate of change for the function f(x) = 3x2 x from the values 5 to 6. a. 1/2 b. 2 c. 34 d. 1/6 Q21. State whether the function f(x) = x(x 7) is a polynomial function or not. If it is, give its degree. If it is not, tell why not. a. Yes degree 2 b. No x is raised to noninteger power c. Yes degree 1 d. No it is a product Q22. Find the intercepts of the function f(x) = 4x5(x + 3) 3. a. xintercepts: 0, 3 yintercept: 0 b. xintercepts: 0, 3 yintercept: 4 c. xintercepts: 0, 3 yintercept: 0 d. xintercepts: 0, 3 yintercept: 4 Q23. For the polynomial f(x) = 4(x 5)(x 6) 3, list each real zero and its multiplicity. Determine whether the graph crosses or touches the xaxis at each xintercept. a. 5, multiplicity 1, touches xaxis 6, multiplicity 3 b. 5, multiplicity 1, touches xaxis 6, multiplicity 3 https://www.umtweb.edu/SRM/CE.aspx?d=E2D8034C803A44A6CB9BBD50984E0EF0D7ACF02EB8070CAD07C0220C3102F1B866B949A10EC50778 8/11 3/2/2017 MATH 105 Exam 2 c. 5, multiplicity 1, crosses xaxis 6, multiplicity 3, crosses xaxis d. 5, multiplicity 1, crosses xaxis 6, multiplicity 3, crosses xaxis Q24. Form a polynomial f(x) with real coefficients of degree 4 and the zeros 2i and 5i. a. f(x) = x4 + 29x2 + 100 b. f(x) = x4 2x3 + 29x2 + 100 c. f(x) = x4 + 29x2 5x + 100 d. f(x) = x4 5x2 + 100 Q25. Solve the inequality algebraically. Express the solution in interval notation. (x 6)/(x + 3) > 0 a. (, 3) (6, ) b. (, 3) c. (6, ) d. (3, 6) Q26. Give the equation of the horizontal asymptote, if any, of the function f(x) = (x2 5)/(25x x4). a. y = 1 b. no horizontal asymptotes c. y = 0 d. y = 5, y = 5 Q27. Find the real solutions of the equation 3x3 x2 + 3x 1 = 0. a. {3, 1/3, 1} b. {1/3} c. {1/3, 1} d. {3, 1/3, 1} Q28. Use the graph to find the vertical asymptotes, if any, of the function. a. none b. x = 2 c. y = 2 d. x = 2, x = 0 Q29. State whether the function f(x) = x(x 9) is a polynomial function or not. If it is, give its degree. If it is not, tell why not. https://www.umtweb.edu/SRM/CE.aspx?d=E2D8034C803A44A6CB9BBD50984E0EF0D7ACF02EB8070CAD07C0220C3102F1B866B949A10EC50778 9/11 3/2/2017 MATH 105 Exam 2 a. Yes degree 2 b. No it is a product c. Yes degree 0 d. Yes degree 1 Q30. For the polynomial f(x) = (1/5)x(x2 5), list each real zero and its multiplicity. Determine whether the graph crosses or touches the xaxis at each xintercept. a. 0, multiplicity 1, touches xaxis 5, multiplicity 1, touches xaxis 5, multiplicity 1, touches xaxis b. 0, multiplicity 1, crosses xaxis 5, multiplicity 1, crosses xaxis 5, multiplicity 1, crosses xaxis c. 5, multiplicity 1, touches xaxis 5, multiplicity 1, touches xaxis d. 0, multiplicity 1 Q31. Find the intercepts of the function f(x) = x2(x 1)(x 6). a. xintercepts: 0, 1, 6 yintercept: 0 b. xintercepts: 0, 1, 6 yintercept: 6 c. xintercepts: 0, 1, 6 yintercept: 0 d. xintercepts: 0, 1, 6 yintercept: 6 Q32. Find the intercepts of the function f(x) = x3 + 3x2 4x 12. a. xintercepts: 2, 2, 3 yintercept: 12 b. xintercepts: 3, 2, 2 yintercept: 12 c. xintercept: 3 yintercept: 12 d. xintercept: 2 yintercept: 12 Q33. Find the real solutions of the equation x4 8x3 + 16x2 + 8x 17 = 0. a. {1, 1} b. {1, 4} c. {4, 4} d. {4, 1} Q34. Find all zeros of the function f(x) = 2x4 + 3x3 + 16x2 + 27x 18 and write the polynomial as a product of linear factors. a. f(x) = (2x 1)(x + 2)(x + 3)(x 3) b. f(x) = (2x + 1)(x 2)(x + 3)(x 3) c. f(x) = (2x 1)(x + 2)(x + 3i)(x 3i) d. f(x) = (2x + 1)(x 2)(x + 3i)(x 3i) Q35. Form a polynomial f(x) with real coefficients of degree 3 and the zeros 1 + i and 10. a. f(x) = x3 10x2 18x 12 b. f(x) = x3 + 8x2 + 20x 18 c. f(x) = x3 + x2 18x + 20 d. f(x) = x3 + 8x2 18x + 20 Q36. Find the domain of the rational function f(x) = (x + 9)/(x2 4x). a. {x|x 2, x 2} b. {x|x 2, x 2, x 9} c. all real numbers d. {x|x 0, x 4} Q37. The function f(x) = x4 5x2 36 has the zero 2i. Find the remaining zeros of the function. a. 2i, 6, 6 b. 2i, 3i, 3i c. 2i, 3, 3 d. 2i, 6i, 6i https://www.umtweb.edu/SRM/CE.aspx?d=E2D8034C803A44A6CB9BBD50984E0EF0D7ACF02EB8070CAD07C0220C3102F1B866B949A10EC50778 10/11 3/2/2017 MATH 105 Exam 2 Q38. Solve the inequality algebraically. Express the solution in interval notation. (9x 5)/(x + 2) 8 a. (2, 13] b. (2, 21) c. (2, 21] d. (2, 13) Q39. Find the power function that the graph of f(x) = (x + 4) 2 resembles for large values of |x|. a. y = x8 b. y = x2 c. y = x4 d. y = x16 Q40. Find the domain of the rational function R(x) = (3x2)/(x2 + 2x 15). a. {x|x 5, 3} b. {x|x 5, 3} c. {x|x 15, 1} d. {x|x 5, 3} Privacy Policy | Contact Us | Copyright 19982017 University of Management and Technology (UMT) | Consumer Information Disclosure https://www.umtweb.edu/SRM/CE.aspx?d=E2D8034C803A44A6CB9BBD50984E0EF0D7ACF02EB8070CAD07C0220C3102F1B866B949A10EC50778 11/11