MATH 107 QUIZ 4
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MATH107Quiz4_Fall_2020.pdf
MATH 107 QUIZ 4 Oct 28, 2020 Instructor: Tim Elsner
NAME: _______________________________ Due: Nov 3rd at 11:59 pm 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 Tue Nov 3rd at 11:59 pm
• 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 x2 −10x and write the solution set in interval notation. (no explanation required) 1. ______
A. [-10, 10]
B. (–, -10] [10, )
C. (–, -10] [0, )
D. [0, 10]
2. (4 pts) Solve 1
𝑥2 − 9𝑥 + 20 < 0 and write the solution set in interval notation. 2. ______
(no explanation required) A. (4, 5)
B. (–, 4) (5, )
C. [-4, -5]
D. (-5, 4)
3. (4 pts) For f (x) = 2x3 – 7x2 + x – 1, use the Intermediate Value Theorem to determine which interval of x must contain a zero of f. (no explanation required) 3. _____
A. Between 0 and 1
B. Between 1 and 2
C. Between 2 and 3
D. Between 3 and 4
4. (4 pts) Translate this sentence about area into a mathematical equation.
The area A of a polygon is directly proportional to the square of the length s of its sides.
5. (8 pts) Look at the graph of the quadratic function and complete the table. [No explanations required.]
Graph Fill in the blanks Equation
State the vertex: (x,y)
____________
State the range:
_____________
State the X interval on
which the function is
decreasing:
_____________
The graph represents which
of the following equations?
Choice:____
A. y = x2 + 4x – 4
B. y = x2 + 4x
C. y = x2 – 4x + 4
D. y = x2 – 4x
6. (6 pts) Each graph below represents a polynomial function. Complete the following table. (no explanation required)
Graph
Graph A
Graph B
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?
7. (12 pts) Let 𝑃(𝑥) = 𝒙𝟑 + 𝟐𝒙𝟐 − 𝒙 − 𝟐 When factored, 𝑃(𝑥) = (𝒙 + 𝟏)(𝒙 − 𝟏)(𝒙 + 𝟐) (a) State the domain
(b) Which sketch illustrates the end behavior of the polynomial function?
Answer: ________
(c) State the y-intercept:
(d) State the real zeros:
(e) State which graph below is the graph of P(x).
GRAPH A. (below) GRAPH B. (below)
GRAPH C. (below) GRAPH D. (below)
A.
B. C. D.
vvvv
vvvv
vvvv vvvv
8. (8 pts) Let 𝑓(𝑥) = x2− 16
x2+ x − 2 . (no explanations required)
(a) State the y-intercept as an ordered pair (x,y)
(b) State the x-intercept(s) as an ordered pair(s) (x,y)
(c) State the vertical asymptote(s). (as an equation)
(d) State the horizontal asymptote. (as an equation)
9. (8 pts) Solve the equation for x. Check all proposed solutions. Show work in solving and in checking, your solution.
x
x−3 −
25
𝑥2−3x = 0
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.
10. _____
A. 𝑓(𝑥) = 𝑥2
𝑥2− 16
B. 𝑓(𝑥) = 𝑥2− 16
𝑥2− 4
C. 𝑓(𝑥) = 𝑥2− 4
𝑥2−16
D. 𝑓(𝑥) = 𝑥2
𝑥2− 4
11. (8 pts) For z = 1 + 5i and w = 3 + i, find z/w. That is, determine 1 + 5𝑖
3 + 𝑖 and simplify as
much as possible, writing the result in the form a + bi, or rational expression, where a and b are real numbers. (hint: use conjugate of the denom) Show work.
12. (8 pts) Consider the equation f(x) = 2x2 − 5x + 6, Find the complex solutions (real and non-real) of the equation using the quadratic formula, 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) = 4250 + 6x for
x 0, and the price-demand function, in dollars per widget, is p(x) = 25 − 0.02x for 0 x 2250.
In Quiz 2, problem #10, we saw that the profit function for this scenario is
P(x) = − 0.02x2 + 19x − 4250.
(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:
Hint: what (x,y) point is the maximum of a parabola (that opens downward)?.
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. (hint: where P(x)=0) Show algebraic work.
