Lynch 2017 Page 1 of 5. Math 150, Fall 2017 Exam 2 Form A Multiple Choice

Transcription

1 Lynch 2017 Page 1 of 5 Math 150, Fall 2017 Exam 2 Form A Multiple Choice Last Name: First Name: Section Number: Student ID number: Directions: 1. No calculators, cell phones, or other electronic devices may be used, and they must all be put away out of sight. 2. There are 11 multiple choice problems on this exam, and each problem is worth 5 points. No partial credit will be given. 3. Together with the other part of the exam there will be a total of 105 points possible. 4. The Scantron will not be returned to you, so please mark your answers on this exam paper. 5. You may not discuss the contents of the exam with anyone until the exam is returned in class. THE AGGIE CODE OF HONOR On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work. Signature: Note: You are authorized to use a pencil, eraser, TAMU Scantron, and your own TAMU student ID; use of anything else is a violation of the honor code. If you need any extra paper, please ask your instructor or TA; do not use your own. Scantron: Make sure the following is filled out correctly on your Scantron: Last Name, First Name, Course #, Section #, UIN, Signature, Date: Oct. 2017, Exam 2, Form A

2 Lynch 2017 Math 150 Exam 2A Page 2 of 5 3 4x if x < 1 1. For f(x) = 7 if 1 x 2 2 x if x > 2 (a) It is undefined. (b) -1 (c) 7 + 2i 2 (d) 3 7 (e) 5 + 2i 7, calculate f(7) + f( 2). f(2) 2. Which of the following is true for the equation 3 x + x 2 y 4 3 y = 12? (a) Symmetric about the origin only (b) Symmetric about the x-axis only (c) Symmetric about the y-axis only (d) Symmetric about the x-axis, y-axis, and origin (e) Not symmetric about the x-axis, y-axis, or origin 3. An open box is constructed from a piece of cardboard that is 7 feet by 4 feet by cutting squares of equal length from each corner and turning up the sides. Write a function for the volume of the cardboard box in terms of the length x of the cutout square. (a) V (x) = (7 x)(4 x) (b) V (x) = x(7 x)(4 x) (c) V (x) = (7 2x)(4 2x) (d) V (x) = x(7 2x)(4 2x) (e) V (x) = 7x x 2

3 Lynch 2017 Math 150 Exam 2A Page 3 of 5 4. Determine the interval where the function f(x) = 6x 2 + 8x + 3 is increasing. (a) (, ) ( (b), 17 ] 3 [ ) 17 (c) 3, [ ) 2 (d) 3, ( (e), 2 ] 3 5. Find the y-intercepts of the equation: x 2 + y 3 + x 3 y 2 = 7. (a) 2 (b) 10 (c) 4, 10 (d) 2, 2 (e) 7, 7 6. The following is the graph of a function f(x). Decide which of the following statements about the function is FALSE. (a) f(x) is one-to-one (b) f(x) is an odd function (c) f(x) is increasing on [ 2, 2] (d) f(x) is decreasing on (, 2] and [2, ) (e) the range of f(x) is (, )

4 Lynch 2017 Math 150 Exam 2A Page 4 of 5 7. Find the domain of the function f(x) = (a) (, 2) (b) (, 4) ( 4, 2] (c) (, 4) ( 4, 3) (3, ) (d) (, 4) ( 4, 2) (2, 3) (3, ) (e) (, 4) [2, 3) (3, ) 2 x x 2 + x Use the graph below to evaluate (f g)(2). (a) 6 (b) 2 (c) 2 (d) 6 (e) Find the perpendicular bisector of the line segment with endpoints ( 6, 1) and ( 2, 5). (a) y = 2 3 x 2 3 (b) y = 2 3 x (c) y = 2 3 x 5 (d) y = 3 2 x + 8 (e) y = 3 2 x 7

5 Lynch 2017 Math 150 Exam 2A Page 5 of Suppose there are two painters, and the first painter can paint a room in 9 hours. If it takes the painters four hours to paint the same room, how long would it take the second painter to paint the room? (a) 4 hours (b) 14 hours (c) 13 2 hours (d) 3 2 hours (e) 36 5 hours 11. The first graph below is the graph of the function f(x). Use transformations to decide which of the following is the graph of g(x) = 3f(2 x) 4. f(x) (a) (b) (c) (d) (e)

6 Lynch, 2017 Page 1 of 6 Math 150, Fall 2017 Exam 2 Form A Work Out Problems Last Name: First Name: Student ID number: Directions: 1. Show all your work neatly and clearly mark your final answer. You must show your work to receive credit. You will be graded not only on the final answer, but also on the quality and correctness of the work leading up to it. 2. No calculators, cell phones, or other electronic devices may be used, and they must all be put away out of sight. 3. There are 10 problems on this exam worth 5 points each. 4. Together with the other part of the exam there will be a total of 105 points possible. It will be graded out of 100, so there are 5 possible bonus points. 5. You may not discuss the contents of the exam with anyone until the exam is returned in class. THE AGGIE CODE OF HONOR On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work. Signature: Note: You are authorized to use a pencil, eraser, and your own TAMU student ID; use of anything else is a violation of the honor code. If you need any extra paper, please ask your instructor or TA; do not use your own. Exam Part Points Earned Points Possible Multiple Choice 55 Page 2: 10 Page 3: 10 Page 4: 10 Page 5: 10 Page 6: 10 Exam 1 Grade (out of 100)

7 Lynch, 2017 Math 150 Exam 2A Page 2 of 6 1. If the distance between (7, 3) and (3, y) is 6, find all possible values for y. y = 2. Suppose the points (5, 3) and ( 1, 1) are the endpoints of the diameter of a circle. Find the equation of the circle. Equation of Circle:

8 Lynch, 2017 Math 150 Exam 2A Page 3 of 6 3. Write the quadratic function f(x) = 5x x 6 in standard form. Find the axis of symmetry of the parabola. Standard Form: Axis of Symmetry: 4. If f(x) = x2 x 2 12, and g(x) = 2 x + 3, find and fully simplify (f g)(x). (f g)(x). Also, find the domain of (f g)(x) = Domain of f g:

9 Lynch, 2017 Math 150 Exam 2A Page 4 of 6 5. State the formula for the difference quotient, and then evaluate the difference quotient for the function f(x) = 4x 2 7x. Fully simplify your answer. Difference Quotient Formula: Difference Quotient for f(x) = 4x 2 7x is 6. List the transformations in order that would be necessary to graph the function f(x) = 2 3 x (You do not need to graph the function.) Transformations (in order): 1) 2) 3) 4)

10 Lynch, 2017 Math 150 Exam 2A Page 5 of 6 7. Suppose the Mississippi River is flowing at a rate of 3 mph. A boat travels up the river for 6 hours. It then returns over the same distance and it only takes 3.5 hours. What would be the boat s speed if it was traveling through still water? Boat s Speed: 8. Algebraically calculate and simplify the inverse of the function f(x) = 2 5 x + 2. Find the domain of f 1 (x). f 1 (x) = Domain of f 1 :

11 Lynch, 2017 Math 150 Exam 2A Page 6 of 6 9. Suppose a baseball is thrown upward, and its distance s in feet from the ground after t seconds is given by s(t) = 16t t + 4. Find the maximum height reached by the ball and the time t it reaches the maximum height. Maximum Height: Time: 10. Find the center and radius of the circle given by the equation 2x 2 + 2y 2 + 8x 6y + 2 = 0. Center: Radius: