MATH107 Quiz2_Fall2016
1. (4 pts) Which of these graphs of relations describe y as a function of x? That is, which are
graphs of functions?
Answer(s): ____________
(There may be more than one graph which represents a function.)
(A)
(B)
(C)
(D)
2. (10 pts) Consider the points (β7, 4) and (3, 6).
(a) Determine the midpoint of the line segment with the given endpoints.
Answer: Midpoint: _______________________________
(b) If the point you found in (a) is the center of a circle, and the other two points are points on the circle,
find the length of the radius of the circle. (That is, find the distance between the center point and a point
on the circle.) Find the exact answer and simplify as much as possible.
Answer: Radius = ____________________________
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3. (12 pts) Consider the following graph of y = f (x). By observing the graph, answer the following
questions in the right-hand column:
(a) State the xintercept(s).
(b) State the yintercept(s).
(c) State the domain.
(d) State the range.
4. (9 pts) Let π(π₯) =
π₯β 9
π₯+2
(a) Calculate π(β3).
Answer: f(-3) = ______________________________
(b) State the domain of the function π(π₯), written in interval notation.
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Answer: Domain (in interval notation): ________________________________
(c) Compute π(π β 1) and simplify as much as possible.
Answer: f(a β 1) = _____________________________________
5. (6 pts) f is a function that takes a real number x and performs the following three steps in the
order given:
(1) Multiply by 4.
(2) Subtract 8.
(3) Take the reciprocal. (That is, make the quantity the denominator of a fraction with numerator 1.)
(a) Find an expression for f (x).
Answer: f(x) = ___________________________________
(b) State the domain of f(x), stated in interval notation
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Answer: Domain (in interval notation): _______________________________
6. (6 pts) Given π(π₯) = π₯ β 3 and π(π₯) = βπ₯ β 1, which of the following is the domain of the
quotient function f / g ?
6._______
A. (1, β)
B. [1, β)
C. [1, 3) βͺ (3, β)
D. (ββ, 3) βͺ (3, β)
7. (6 pts) For income x (in dollars), a particular state's income tax T (in dollars) is given by
0.02π₯
ππ 0 β€ π₯ β€ 2,000
π(π₯) = { 40 + 0.03(π₯ β 2000) ππ 2,000 < π₯ β€ 4,000
100 + 0.04(π₯ β 4,000)
ππ π₯ > 4,000
(a) What is the tax on an income of $3,200?
Answer: Tax = __________________________________
(b) What is the tax on an income of $32,000?
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Answer: Tax = __________________________________
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8. (20 pts) Let y = 8 ο 2x2.
(a) Find the x-intercept(s) of the graph of the equation, if any exist.
Answer: x-intercept(s): ___________________________________
(b) Find the y-intercept(s) of the graph of the equation, if any exist.
Answer: y-intercept(s): ___________________________________
(c) Create a table of sample points on the graph of the equation. (Include at least five points.)
x
y
(x, y)
(d) Create a graph of the equation. (You may use the grid shown below, hand-draw (with the aid of your
graphing calculator) and scan, or use the free Desmos graphing calculator described under Course Resources
(Mathematics Communication and Graphing sub-tab) of your course to generate a graph, save as a jpg and
attach.)
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(e) Is the graph symmetric with respect to the y-axis? _____ (yes or no).
If no, state a point on the graph of the equation whose reflection fails to be on the graph, as done in
section 1.2 homework in the textbook.
(f) Is the graph symmetric with respect to the x-axis? _____ (yes or no).
If no, state a point on the graph of the equation whose reflection fails to be on the graph, as done in
section 1.2 homework in the textbook.
(g) Is the graph symmetric with respect to the origin? _____ (yes or no).
If no, state a point on the graph of the equation whose reflection fails to be on the graph, as done in
section 1.2 homework in the textbook.
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9. (12 pts) Let f (x) = 5x2 β 7x + 8 and g(x) = 1 β 3x.
(a) Find the difference function (f β g)(x) and simplify the results. .
Answer: (f β g)(x) = ______________________________________________
(b) Find (g β f)(β1).
Answer: (g β f)(-1) = ______________________________________________
(c) Find (f βg)( β1). (That is, the product function of βfβ times βgβ, evaluated at x = -1).
Answer: (f βg)( β1) = ____________________________________
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10. (15 pts) The cost, in dollars, for a company to produce x widgets is given by:
C(x) = 4700 + 5.20x for x ο³ 0.
The price-demand function, in dollars per widget, is p(x) = 40 ο 0.02x for 0 ο£ x ο£ 2000.
(REFER TO PAGE 82 OF THE TEXT FOR THE DEFINITIONS AND DESCRIPTIONS
ON HOW TO WORK THIS PROBLEM).
(a) Find C(500).
Answer: C(500) = ________________________________________
(b) Find πΆΜ
(500). (Note that πΆΜ
(x) is the average cost function.)
Answer: πΆΜ
(500) = _________________________________________
(c) Find and simplify the expression for the revenue function R(x).
Answer: R(x) = ___________________________________________
(d) Find and simplify the expression for the profit function P(x).
Answer: P(x) = ___________________________________________
(e) Find P(500), where P(x) is the profit function in part (d).
Answer: P(500) = _____________________________________
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