Precalculus
QUIZ 1 Professor: Ms. Chowdhury MATH 115 Fall 2018 Name___________________________________ Date ________________ INSTRUCTIONS
The quiz is worth 55 points. There are 20 multiple choice (2 points) and 5 (3 points) short answer problems.
This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone.
You must show all of your work to receive full credit. If you do not show work, you may earn only partial or no credit at the discretion of the professor.
Please type your answers on the table in the separate answer sheet.Scanned handwritten work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module.
If you have any questions, please contact me by e-mail.
Please record your answer in the table below.
I have completed this assignment myself, working independently and not consulting anyone except the instructor and my notes. (If this part is not completed, you will receive a zero for the quiz)
Sign here __________________________________________ Date _______________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the equation defines y as a function of x.
1) x2 + y = 64
A) y is a function of x B) y is not a function of x
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2) x = y2
A) y is a function of x B) y is not a function of x
Determine whether the given function is even, odd, or neither.
3) f(x) = x3 - 5x
A) Even B) Odd C) Neither
4) f(x) = x3 + x2 + 5
A) Neither B) Odd C) Even
Evaluate the function at the given value of the independent variable and simplify.
5) f(x) = 5x2 - 5x - 1; f(x - 1)
A) 5x2 - 15x + 9 B) 5x2 - 15x - 1 C) 5x2 - 10x - 1 D) -15x2 + 5x + 9
6) f(x) = x3 - 3 x2 + 3
; f(3)
A) 1 2
B) 2 C) 9 4
D) 8 3
Evaluate the piecewise function at the given value of the independent variable.
7)
f(x) = -4x + 2 if x < -4
4x - 1 if x -4
Determine f(-5).
A) 22 B) 21 C) 20 D) -18
8)
g(x) = x2 - 1 x + 7
if x -7
x - 2 if x = -7
Determine g(4).
A) 3 11
B) 15 11 C) 4 D) 2
Find and simplify the difference quotient f(x + h) - f(x) h
, h 0 for the given function.
9) f(x) = 6x2
A) 12 h
+ x + 6h B) 6(2x2 + 2xh + h2)
h C) 6 D) 6(2x+h)
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Find functions f and g so that h(x) = (f g)(x).
10) h(x) = 1
x2 - 9
A) f(x) = 1/x, g(x) = x2 - 9 B) f(x) = 1/x2, g(x) = x - 9
C) f(x) = 1/9, g(x) = x2 - 9 D) f(x) = 1/x2, g(x) = - 1/9
11) h(x) = 1
6x + 2
A) f(x) = 1/x, g(x) = 6x + 2 B) f(x) = 6x + 2, g(x) = 1
C) f(x) = 1/ x, g(x) = 6x + 2 D) f(x) = 1, g(x) = 6 + 2
Find the domain of the composite function f g.
12) f(x) = 6
x + 8 , g(x) = x + 7
A) (- , -8) (-8, -7) (-7, ) B) (- , )
C) (- , -15) (-15, ) D) (- , -8) (-8, )
For the given functions f and g , find the indicated composition.
13) f(x) = x2 - 2x + 5, g(x) = x2 + 2x - 4 (f g)(3)
A) 47 B) 85 C) 104 D) 142
Given functions f and g, perform the indicated operations.
14) f(x) = 4 - 2x, g(x) = -7x + 2 Find f + g.
A) 5x + 6 B) -3x C) -9x + 6 D) -7x + 4
Use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a function that is neither even nor odd.
15)
A) Odd B) Even C) Neither
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16)
A) Neither B) Even C) Odd
Use the graph of the given function to find any relative maxima and relative minima.
17) f(x) = x3 - 12x + 2
A) maximum: (2, -14); minimum: (-2, 18) B) no maximum or minimum
C) minimum: (2, -14); maximum: (-2, 18) D) maximum: (-2, 18) and (0, 0); minimum: (2, -14)
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Use the graph to determine the function's domain and range.
18)
A) domain: [3, 5] range: (- , )
B) domain: (- , ) range: [3, 5]
C) domain: [0, 5] range: (- , )
D) domain: (- , ) range: [0, 5]
Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
19)
A) function B) not a function
Write the standard form of the equation of the circle with the given center and radius.
20) (10, 7); 7
A) (x + 10)2 + (y + 7)2 = 7 B) (x + 7)2 + (y + 10)2 = 49
C) (x - 7)2 + (y - 10)2 = 49 D) (x - 10)2 + (y - 7)2 = 7
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations of this graph to graph the given function. Explain the transformations verbally as well.
21) g(x) = - 1 3
(x - 3)2 - 3
Find the distance between the pair of points.
22) (0, 0) and (4, 5)
Graph the equation and state the domain and range using interval notation.
23) (x - 2)2 + (y - 3)2 = 25
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Identify the intervals where the function is increasing, decreasing, and constant. Use interval notation.
24)
Solve the problem.
25) Suppose a life insurance policy costs $32 for the first unit of coverage and then $8 for each additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage. What will 10 units of coverage cost?
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