MAT141 Review I for Final Exam Blitzer 1 1. Which of the following is the square that is completed when solving the equation, 20 2 20 7xx, by completing the square? a. 225x b. 225x 1__________ c. 25x d. 25x 2. Express the perimeter of a rectangle whose length is 5 more than its width in terms of its width, w. a. 4 10Pw b. 53Pw 2_________ c. 25Pw d. 45Pw 3. Find all real solutions of the equation 4 5 4xx. a.1,11x b. 0x c.11x d. There are no real solutions. 3.________ 4. Find the maximum value of 2( ) 2 12 20.f x x x a. (3) 2f b. ( 2) 3f c. ( 3) 2f 4________ d. (2) 3f 5. Which of the following is the range of( ) 4f x x? a. [0, ) b. [4, ) c. ,4 5_______ d. , 6. Find the slope and y-intercept of the line 2 5 4xy. a. 2, 0,45m b. 5, 0,42m c. 24, 0,55m 6_____ d. 54, 0,25mMAT141 Review I for Final Exam Blitzer 2 7. Given 2( ) ( 1)f x xand1()1gxx, which of the following isf g x? a. 211f g xx b. 1, 1f g x x x c. 2,11xf g x xx 7_____ d. 22,11xf g x xx 8. If the inverse of a function f exists on the interval 0,2 and 1(0) 1f and1(2) 4f, then which of the following is true? a. The domain of f is [0, 2]. b. 0 and 2 are in the domain of f. 8_____ c. The point 4,2is on the graph of f. d. f is a decreasing function. 9. Solve the inequality,8 12 4 16x, and express the solution in interval notation. a. 5,1 b. 1,5 9_____ c. 5,1 d. 1,5 10. Solve 5 3 6x. a. 93 or 55xx b. 93,55 c. 93,55 10_____ d. 39and 55xxMAT141 Review I for Final Exam Blitzer 3 11. Which of the following is true of the graph of the quadratic function 2( ) 3 2 3f x x? a. The vertex is in quadrant II. b. The axis of symmetry is2x. 11_____ c. The minimum is3. d. There are no x-intercepts. 12. Find the equation of a quadratic function with the vertex( 1, 2), that passes through the point ( 3,10), and opens upward. a. 2( ) 3 2 1f x x x b. 2( ) 3 2 1f x x x c. 2( ) 3 6 1f x x x 12.______ d. 2( ) 3 2 5f x x x 13. Use long division to dividex x x32 4 3chbg. a. x x23 7 + 253x b. x x25 11 + 333x 13_____ c. x x23 11 – 273x d. x x25 15 – 413x 14. Solve: 4249 25 0xx. a. 2549x b 50,7x c 4925x d 70,5x 14.______ 15. An ellipse has vertices at 5, 0bg and foci at4, 0bg. Find the equation of the ellipse in standard form. a. x y2 225 91 b. x y2 29 251 c. x y2 216 251 d. x y2 225 161 15.______MAT141 Review I for Final Exam Blitzer 4 16. Find the domain of the function( ) 3 10f x x. a. 103x b. 0x c. 103x d. 0x 16.______ 17. Find the inverse of the function 22()43xfxx . a. 134()22xfxx b. 142()32xfxx 17.______ c. 134()22xfxx d. 122()34xfxx 18. Find the slope-intercept form of the equation of the line through the point– , ,6 3 bgparallel to the line3 7 3xy. a. 3377yx b. 7733yx 18.______ c. 3773yx d. 3377yx 19. Find the equation of the parabola with vertex at the origin that passes through the point (4,16) and opens upward. a. x y2 b. y x2 19.______ c. y x2 d. x y2MAT141 Review I for Final Exam Blitzer 5 20. If2( ) 1f x xand( ) 6g x x, find( ( ))f g x. a. 261x b. 236 1x c. 231x d. 236 1x 20.______ 21. Determine the vertices and foci of the graph of x y2 264 251. a. Vertices: , 08bg Foci: , 089d i b. Vertices: 0, 8bg Foci: 0, FHGIKJ89 21.______ c. Vertices: , 0FHGIKJ6425 Foci: 0, FHGIKJ89 d. Vertices: , 06425FHGIKJ Foci: , 089d i 22. Find the right-hand and left-hand behavior of the polynomial function 72( ) 2 2 6f x x x. a. Falls to the left and falls to the right. b. Rises to the left and falls to the right. c. Falls to the left and rises to the right. 22.______ d. Rises to the left and rises to the right. 23. Solve 4251xx. a. 9,05x b. 4,15x c. 0x d. 1x 23.______MAT141 Review I for Final Exam Blitzer 6 Use the graph below to answer questions 24-30. Put your answers on the line at the right. 24. True or false: The degree of this polynomial is even. ___________ 25. True or false: The y – intercept is at (6,0). _______________ 26. Describe the end-behavior of the polynomial. 27. List all the roots of this polynomial. 28. On what intervals is the function increasing? Use interval notation and approximate where you need to. 29. True or false and WHY: The function is one-to-one. 30. Where is f(x) <0? Use interval notation. x yMAT141 Review I for Final Exam Blitzer 7 KEY Review for Final 1. d 24. T 2. a 25. F 3. c 26. rises to the left and to the right 4. a (as , ( )x f x and as , ( )x f x) 5. b 6. c 27. ( 2,0),( 1,0),(1,0),(2,0) 7. d 8. c 28. ( 1.5,0),(1.5, ) 9. d 10. c 29. No because it fails the horizontal line test. 11. b 12. c 30. ( 2, 1),(1,2) 13. a 14. b 15. a 16. a 17. b 18. d 19. c 20. d 21. a 22. c 23.