MAT135 Review for Test 4 Dugopolski Sections 7.5, 7.6, 8.1, 8.2, 8.3, 8.4

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1 Sections 7.5, 7.6, 8.1, 8., 8., Use the discriminant to determine the number and type(s) of solutions for 4x 8x 4 0. One real solution B. One complex solution Two real solutions Two complex solutions. Simplify: B. 5 i 5 i 5. An object is thrown upward from 96 feet above the ground with an initial velocity of 80 ft/sec. The height of the object, in feet, after t seconds is given by h( t) 16t 80t 96. After how many seconds does the object hit the ground? 6.0 seconds B seconds 5.0 seconds.0 seconds 4. If B. f ( x) x and g( x) 1x 1, where is f ( x) g( x )? Evaluate and write the answer in standard form: 9 7 i 5 i. 5 i B. i 5 i i 1 6 1

2 Sections 7.5, 7.6, 8.1, 8., 8., Find the domain and range of the graph below. You may assume each tick mark represents one unit. y x Domain (, ) Range [5, ) B. Domain [5, ) Range (, ) Domain (, ) Range (,5] Domain (,5] Range (, ) 7. What is true of f ( x) x x 4? The y-intercept is (0, 4). B. It is a parabola that opens downward. The vertex is at (,4). f( x ) has no real roots. 8. Simplify: ( 10 16) ( 4). 8 1i B. 8 4i 1i 1 1i 9. If f ( x) x 8 and g( x) 18 x, where is f ( x) g( x )? x, x 7 B. x, x 7 x 7, x x 7, x

3 Sections 7.5, 7.6, 8.1, 8., 8., Solve: 5 x( x 4) (4x )( x 4). x B. x 4 x 4, x x 4, x 11. Use the quadratic formula to solve: x 10x 9 0. x 7, x B. x 10 4i x 5 i x 5 i 1. Does or minimum value? f ( x) 4 8x 4x open upward or downward, and does it have a maximum f( x ) opens downward and has a minimum value. B. f( x ) opens downward and has a maximum value. f( x ) opens upward and has a minimum value. f( x ) opens upward and has a maximum value. 1. If the area of a square is represented by x 4x 4, find an expression for each side. x B. x ( x ) ( x ) 14. Solve: y 56. { 16,16} B. {16} { 16} {0, 16} 15. What must be added to both sides of the equation square? x 18x 0 to complete the 0 B none of these 16. Solve: (4t 6) 11. t 5 4 B. t 11 6 t t

4 Sections 7.5, 7.6, 8.1, 8., 8., What is the range of the function shown below? You may assume that each tick mark represents one unit. y x [, ) B. [, ) (,] (, ] 18. Solve: ( x 9)( x 8) 16. x 9, x 8 B. x 9, x 8 x 8, x 7 x 7, x An object is thrown upward from 96 feet above the ground with an initial velocity of 80 ft/sec. The height of the object, in feet, after t seconds is given by h( t) 16t 80t 96. After how many seconds does the object reach its maximum height?.5 seconds B. 5.0 seconds 5.0 seconds 11.0 seconds 0. What is true of f ( x) x x 7? It has a maximum value at ( 6, 1). B. It has a minimum value at ( 6, 1). It has a minimum value at ( 1, 6). It has a maximum value at ( 1, 6). 4

5 Sections 7.5, 7.6, 8.1, 8., 8., A rug must fit into a room so that there is a border of equal width on all sides. If the room is 8 feet by feet and the area of the rug is 4 square feet, how wide will the border be? 5.0 feet B. 4.5 feet.5 feet.5 feet. What is the quadratic equation that has roots at B. 1x 7x 1 0 1x 7x 1 0 1x x 1 0 x x x and x 4. What are the x-intercepts of f ( x) x x 18? (6,0),(,0) B. (6,0),(,0) ( 6,0),(,0) ( 6,0),(,0) 4. The temperature, t, in degrees Farenheit, of a certain chemical reaction can be approximated by the function t( s) s 6s 70, where s is the number of seconds after the reaction begins. What is the lowest temperature possible, and when will it occur? The lowest temperature will be B. The lowest temperature will be The lowest temperature will be The lowest temperature will be 5. Find the domain and range of Domain: (, ) Range: (,5] B. Domain: (, ) Range: [5, ) Domain: (,5] Range: (, ) Domain: (, ) Range: [ 5, ) F after 6 seconds. 0 8 F after 1 seconds. 0 8 F after 6 seconds F after seconds. f ( x) x 4x 6. What is the vertex of f ( x) 4x x 67? ( 4, ) B. (4,) (, 4) (,4) 5

6 Sections 7.5, 7.6, 8.1, 8., 8., What is the minimum value of the function graphed below? You may assume that each tick mark represents one unit. y x y 1 B. y 9 y y 4 8. A ball is thrown upward with an initial velocity of 56 ft/sec. The height, in feet, after t seconds is approximated by h( t) t(56 16 t ). What is the maximum height attained by the ball? 4.6 feet B. 65. feet 98 feet 49 feet 9. 6x 17x 0 has one real solution. B. two real solutions. two complex solutions. no solution. 0. Use the quadratic formula to solve x x 5x. 1 5 x B. 1 5 x x 1 5 x 1 5 6

7 Sections 7.5, 7.6, 8.1, 8., 8., Which of the following statements is true about f ( x) x 9x 0? The x-intercepts are (4,0) and ( 5,0). B. The y-intercept is (0, 0). 9 1 The vertex is, 4. Both B and C are true.. Solve 1 A r for r. A r B. r A. Solve: 5x 4 1 x. A r {,6} B. 9 1 r A 4. Multiply: (4 81)(9 100) i B i 16 11i What is true of the graph shown below? y x It has imaginary roots. B. The range is (, ). It is a function. The y-intercept is (,0). 7

8 Sections 7.5, 7.6, 8.1, 8., 8., 8.4 KEY Review for Test 4 1. A 0. A. D 1. D. A. C 4. C. C 5. B 4. A 6. C 5. C 7. D 8. A 9. B 10. D 11. C 1. C 1. A 14. A 15. B 16. D 17. C 18. C 19. A 0. D 1. A. C. B 4. C 5. A 6. B 7. B 8. D 9. B 8

9 Sections 7.5, 7.6, 8.1, 8., 8., 8.4 9

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