g-Quiz4 for MathExpert121
momma0807
quiz_4_math_107.pdf
MATH 107 QUIZ 4 July, 2016 Instructor: A. Bluiett NAME: _______________________________ I have completed this assignment myself, working independently and not consulting anyone except the instructor.
INSTRUCTIONS The quiz is worth 100 points. There are 13 problems. This quiz is open book and open notes. This means that
you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz no later than Sunday, July 24.
Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work.
General quiz tips and instructions for submitting work are posted in the Quizzes module. If you have any questions, please contact me by e-mail.
1. (4 pts) Solve the inequality x
2 +5x+4 > 0 and write the solution set in interval notation.
(no explanation required) A. (-4, -1) B. (–, -4) (-4,-1) (-1, ) C. (–, -4) (-1, )
D. (–, -4)
2. (4 pts) Solve 0 4
2142
x
xx and write the solution set in interval notation.
(no explanation required)
3. (4 pts) For f (x) = x 3 – 2x
2 – 7, use the Intermediate Value Theorem to determine which
interval must contain a zero of f. (no explanation required) A. Between 1 and 2 B. Between 0 and 1 C. Between 3 and 4 D. Between 2 and 3
4. (4 pts) Translate this sentence about area into a mathematical equation. The area A of a regular hexagon is directly proportional to the product of the number of sides and the square of the length s of its sides.
5. (8 pts) Look at the graph of the quadratic function
Graph
6. (6 pts) Each graph below represents a polynomial function. Complete the following table. (no explanation required)
Graph
Is the degree of the polynomial odd or even? (choose one)
Is the leading coefficient of the polynomial positive or negative? (choose one)
How many real number zeros are there?
of the quadratic function and complete the table. [No explanations required. Fill in the blanks Equation
State the vertex:
____________ State the range:
____________ State the interval on which the function is decreasing: ____________
_
The graph represents which of the following equations? Choice:____ A. B. C. D.
pts) Each graph below represents a polynomial function. Complete the following table.
Graph A
Graph B
No explanations required.] Equation
The graph represents which of the following equations?
Choice:____
A. y = -x 2 + 6x – 1
B. y = –2x 2 – 4x + 1
C. y = x 2 - 6x + 1
D. y = x 2 + 8x – 1
pts) Each graph below represents a polynomial function. Complete the following table.
Graph B
7. (12 pts) Let �(�) = −�� + 4.5�
(a) State the real zeros: (b) Which sketch illustrates the end behavior
(d) State the domain. (e) State which graph below is the graph of
GRAPH A. (below)
GRAPH C. (below)
A.
B.
�� − 0.5� − 6 When factored, �(�) = −(� + 1)
end behavior of the polynomial function?
Answer: ________
(c) State the
which graph below is the graph of P(x).
GRAPH B. (below)
GRAPH D. (below)
C. D. vvvv
) �� − �
� � (� − 4)
Answer: ________
State the y-intercept:
8. (8 pts) Let 25
164 )(
2
2
x
x xf . (no explanations required)
(a) State the y-intercept. (b) State the x-intercept(s). (c) State the vertical asymptote(s). (d) State the horizontal asymptote. 9. (8 pts) Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.
3 3
3 3
w
w
ww
10. (8 pts) Which of the following functions is represented by the graph shown below? Explain your answer choice. Be sure to take the asymptotes into account in your explanation.
A. �(�) = �
��� ��
B. �(�) = �
��� ��
C. �(�) = ��
��� ��
D. �(�) = �
��� ��
11. (8 pts) For z = 4 3i and w = 7 i, find w/z. That is, determine � � �
� � �� and simplify as
much as possible, writing the result in the form a + bi, where a and b are real numbers. Show work.
12. (8 pts) Consider the equation 10x 2 + 40 = 32x. Find the complex solutions (real and non-
real) of the equation, and simplify as much as possible. Show work. 13. (18 pts)
The cost, in dollars, for a company to produce x widgets is given by C(x) = 4200 + 5.00x for x 0, and the price-demand function, in dollars per widget, is p(x) = 38 0.02x for 0 x 1900. In Quiz 2, problem #10, we saw that the profit function for this scenario is P(x) = 0.02x
2 + 33.00x 4200g.
(a) The profit function is a quadratic function and so its graph is a parabola.
Does the parabola open up or down? __________ (b) Find the vertex of the profit function P(x) using algebra. Show algebraic work. (c) State the maximum profit and the number of widgets which yield that maximum profit: The maximum profit is _______________ when ____________ widgets are produced and sold.
(d) Determine the price to charge per widget in order to maximize profit.
(e) Find and interpret the break-even points. Show algebraic work.
