MAT141 Review for Test III BlitzerChapter 2 Sec. 2.3-2.6Chap. 3 Sec. 3.1-3.31. Determine whether the function2( ) 2 7f x x x=- - - has a maximum or minimum value and find the coordinates of that point.a. Minimum at (-6,-1)b. Maximum at (-6,-1)c. Minimum at (-1,-6)d. Maximum at (-1,-6)2. Perform the indicated operation and write the result in standard form:( )4 4 9- - -.a.26 8i i- +b.26 8i i+c. 6 + 8id. 6 – 8i3. Which of the following is a polynomial function?a.62( ) 4f xx= -b.368( )xf xx-=c.42( )8xf x-=d.77( ) 10 3f x x xx= + +4. Solve:1 3(6 2) 4 3x + - =.a. 47/6b. 341/6c. 19/6d. no solution5. Find the value(s) that satisfy2 3 1 1x x+ - + =.a. x = -1, x = 3b. x = 3c. x = -3, x = -1d. no solution6. What is the end behavior of the graph of3( ) ( 1)( 3)( 5)f x x x x= + + +?a. It falls to the left and rises to the right.Fall 2008 1 MAT141MAT141 Review for Test III BlitzerChapter 2 Sec. 2.3-2.6Chap. 3 Sec. 3.1-3.3b. It falls to the left and falls to the right.c. It rises to the left and falls right.d. It rises to the left and rises to the right.7. 0.5 16C x= +gives the relationship between cost, C, in thousands of dollars and yearlyattendance at State University, where x represents years after 2002. If$20,000 $22,000C� �, what years represent the range of x?a.2009 2013x� �b.2010 2014x� �c.2011 2015x� �d.2011 2013x� �8. Divide:3 24 19 33 186x x xx- - + ++.a.24 6 3x x- +b.24 6 3x x+ -c.24 5 3x x- + +d.24 5 3x x- - -9. If2( ) 6 2, ( ) , find the value(s) for which ( )( )=196f x x g x x g f x= + = o.a. x = 2b. x = 97/3c. x = -8/3d. x = 2, x = -8/310. What is added to both sides to complete the square of26 40x x+ =?a.3/ 2b.9 / 4c. 9d. 411. Which interval belongs to the solution of26 40x x+ <?a. (-20, -18)b. [6, 8]c. [8, ∞)d. [-1, 1]12. On which interval(s) would you expect to find a zero for the polynomial?X Y10 1Fall 2008 2 MAT141MAT141 Review for Test III BlitzerChapter 2 Sec. 2.3-2.6Chap. 3 Sec. 3.1-3.31 -32 -53 1a.(0,1), (2,3)b.( 3,1),( 5,1)- -c.(0,1), (1, 2)d.( )1, 213. Perform the operation and write the answer in standard form: 103ii+.a. 1+3ib. -1+3ic. 1+10id. 1-3i14. Find the vertex of the parabola2( ) 6 ( 2)f x x= - +.a. (2, 6)b. (-2, 6)c. (6, 2)d. (6, -2)15. You invest $10,000 in two funds, paying 6% and 11%, respectively. How much should you invest in the fund paying 6% if the total interest at the end of the year should be $900?a. $3,000b. $4,000c. $5,000d. $6,00016. Use the Intermediate Value Theorem to determine which of the following pairs determine endpoints of intervals that contain an x-intercept.a.( 1) 4, (0) 2f f- =- =-b.(1) 62, ( 3) 2f f= - =c.( 2) 49, ( 1) 7f f- =- - =-d.( 1) 12, (0) 3f f- =- =17. Solve: 2 13 35 6 0x x- + =.a. x = -27, x = -8Fall 2008 3 MAT141MAT141 Review for Test III BlitzerChapter 2 Sec. 2.3-2.6Chap. 3 Sec. 3.1-3.3b. x = 8, x = 27c. x = 2, x = 3d. x = -3, x = -218. Which of the following is not true for( ) ( 2)( 1)( 1)f x x x x= - - +?a. There are 3 real zeros.b. There are three turning points.c. The y-intercept is (0, 2).d. This is a third degree polynomial.19. If ( ) 5 2f x x= + and( ) 4 4g x x= +, where is f(x) > g(x)?a. (-∞, 2]b.(6, )� c.[2, )� d.(2, )� 20. When a number is subtracted from -7, the absolute value of the difference is more than 3. Which set of numbers satisfies this condition?a.( , 10) [4, )-�-ȥb.( , 4) (10, )-�-ȥc.( , 10) ( 4, )- �- � - �d.( )10, 4- -21. What is true of the graph of2( ) 7 ( 2)f x x= + +?a. The range is[7, )�.b. There are two real zeros.c. The maximum value is 7.d. The axis of symmetry is x = 7.22. Find all the zeros of3 2( ) 6 6f x x x x= + - -.a. x = 1, x = -6, x = 6b. x = -1, x = 1, x = -6c. x = -6, x = 6d. x = 6, x = 123. Solve:4 753x xx x- ++ =.a.25 /13; 0, 3x x x= � �b.11/15x =c.10, 0x x=- �d.25 /13; 0x x= �24. Use synthetic division and the Remainder Theorem to find ( 3)f -if Fall 2008 4 MAT141MAT141 Review for Test III BlitzerChapter 2 Sec. 2.3-2.6Chap. 3 Sec. 3.1-3.33 2( ) 3 5 5 9f x x x x= - - +.a. -102b. -60 c. -24d. -1825. Given21 1 1( ) , ( ) and ( )6 5 11 30f x g x h xx x x x= = =-+ + + +, if the sum of the function values of f and 4 times the function values of g equals the function values of h, what is x?a. 0b. -6c. 5d. no solution26. Use the discriminant to determine the number and type of solution(s) for23 2 1x x= -.a. one real solutionb. two complex solutionsc. two real solutionsd. It cannot be determined.Use the graph below to answer questions 27-35 below.( )y g x=Fall 2008 5 MAT141xyMAT141 Review for Test III BlitzerChapter 2 Sec. 2.3-2.6Chap. 3 Sec. 3.1-3.327. What is the probable degree of this function?28. Write a possible equation for( )y g x= .29. Describe the zeros of ( )y g x=and the multiplicity of each.30. On what interval(s) is ( )y g x=<0? 31. Is ( )y g x= a one to one function?32. Is( 5)g - positive or negative?33. What is the domain of( )y g x=?34. How many times does the graph of 2( )f x x= intersect( )y g x=?35. On what interval(s) is ( )y g x= increasing?Answer Key for Review Test III1. d 14. b 27. 32. c 15. b 28. ( ) ( 3)( 2)g x x x x=- - +3. c 16. d29. The zeros at 2, 0, 3x x x=- = = all have multiplicity one.4. b 17. b5. a 18. b 30. ( 2,0), (3, )- �6. a 19. d 31. No: it fails the horizontal line test.7. b 20. cFall 2008 6 MAT141MAT141 Review for Test III BlitzerChapter 2 Sec. 2.3-2.6Chap. 3 Sec. 3.1-3.38. c 21. a 32. Positive9. d 22. b 33. ( , )- ��10. c 23. d 34. three times11. d 24. a12. a 25. d 35. approximately ( 1, 2)-13. a 26. bFall 2008 7