MATH107 Interval Notation Intermediate Value Theorem College Algebra Quiz 4

Please see problems on attachment (13 problems to solve)

MATH 107 QUIZ 4
NAME: _______________________________
April, 2019
Instructor: S. Sands
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, April 28.
• 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 9x
≥ x2 and write the solution set in interval notation.
(no explanation required)
A.
B.
C.
D.
2. (4 pts) Solve
1. ______
(– , 9]
[9, )
(–, 0]  [9, )
[0, 9]
𝑥+3
𝑥 2 − 4𝑥 − 5
≥ 0 and write the solution set in interval notation.
2. ______
(no explanation required)
A.
B.
C.
D.
(–1, 5)
[–3, )
[–3, –1)  (5, )
(–, –3]  (5, )
3. (4 pts) For f (x) = 2×5 – 5×3 – 3, use the Intermediate Value Theorem to determine which
interval 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) A car’s brakes are applied. Translate the following sentence into a mathematical
equation: The stopping distance D of the car is directly proportional to the square of the speed s.
5. (10 pts) View the graph of the quadratic function y = f (x) and complete the table. [No explanations required.]
Fill in the blanks
Vertex: ____________
Range: _____________
Interval on which the function is decreasing:____________
The graph represents which of the following equations?
Choice:____
A.
B.
C.
D.
2
𝑦 = −𝑥 + 6𝑥 − 10
𝑦 = −2𝑥 2 − 12𝑥 − 10
𝑦 = −2𝑥 2 + 12𝑥 − 10
𝑦 = 2𝑥 2 + 12𝑥 − 10
For what x values is f (x) ≥ 0 ?
A.
B.
C.
D.
Choice:____
[–5, –1]
(–, 8]
[0, 8]
[0, )
6. (6 pts) Each graph below represents a polynomial function, with the graph continuing in the
directions indicated at the ends of the graph. Complete the following table. (no explanation required)
Graph
Graph A
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?
Graph B
7. (12 pts) Let 𝑃(𝑥)
1
= −6𝑥 3 − 3𝑥 2 + 6𝑥 + 3. When factored, 𝑃(𝑥) = −6(𝑥 − 1)(𝑥 + 1) (𝑥 + 2).
(a) State the domain.
(b) Which sketch illustrates the end behavior of the polynomial function?
A.
B.
vvvv
C.
vvvv
D.
vvvv
vvvv
(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)
Answer: ________
8. (8 pts) Let
𝑓(𝑥 ) =
10𝑥 + 1
2𝑥 + 3
. (no explanations required)
(a) State the x-intercept(s).
(b) State the y-intercept.
(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.
𝑥−4
𝑥 −2
+
18
𝑥2
+ 5𝑥 −14
=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) =
B. 𝑓(𝑥) =
C. 𝑓(𝑥) =
D. 𝑓 (𝑥 ) =
𝑥−1
𝑥 2 − 2𝑥
𝑥−1
𝑥 2 + 2𝑥
𝑥−1
𝑥−2
𝑥2 − 1
𝑥 2 − 2𝑥
11. (6 pts) For z = 9 + 2i and w = 4 − 3i, find z/w. That is, determine
9 + 2𝑖
and simplify as
4 − 3𝑖
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 5×2 + 20 = 16x. Find the complex solutions (real and nonreal) of the equation, and simplify as much as possible. Show work.
13. (18 pts) Company XYZ manufactures and sells widgets. The cost, in dollars, to produce x widgets is
given by C(x) = 2602 + 3.60x for x  0, and the price-demand function, in dollars per widget, is
p(x) = 24 − 0.02x.
In Quiz 2, problem #10, we saw that the profit function for this scenario is
P(x) = − 0.02×2 + 20.40x − 2602.
(a) The graph of the profit function 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) In order to earn exactly $2,400 profit, how many widgets must be made and sold? Show algebraic
work.
(f) In order to earn at least $2,400 profit, how many widgets must be made and sold? Write a sentence
to answer the question.