question archive My name indicates that I have completed this assignment myself, working independently and consulting no one except the instructor
My name indicates that I have completed this assignment myself, working independently and consulting no one except the instructor
Subject:MathPrice: Bought3
My name indicates that I have completed this assignment myself, working independently and consulting no one except the instructor.
INSTRUCTIONS
· The quiz is worth 50 points. There are 9 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 the due date.
· 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 need more room, just add it into the file.
· If you have any questions about the quiz, please ask on the Discussion Board or email me at jill.whealon@faculty.umgc.edu
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): ____________
( no explanation required .) (There may be more than one graph which represents a function.)
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(A)
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(B)
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(C)
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(D)
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2. (4 pts) Consider the points (–3, 5) and (–9, 12). Find the distance between the 2 points and also the midpoint of the line segment with the given endpoints.
3. (8 pts) Consider the following graph of y = f (x).
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(no explanations required)
(a) State the x-intercept(s) in ordered pair format.
(b) State the y-intercept(s) in ordered pair format.
(c) State the domain.
(d) State the range.
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4. (7 pts) Let f(x) =
(a) Calculate f(-2)
(b) State the domain of f(x)
(c) Find f(a + 1) and simplify as much as possible.
5. ( 4 pts) f is a function that takes a real number x and performs these four steps in the order given:
(1) Multiply by 5.
(2) Add 11.
(3) Take the square root.
(4) Take the reciprocal. (That is, make the quantity the denominator of a fraction with numerator 1.)
(a) Find an expression for f (x).
(b) State the domain of f.
6. (3 pts) Given f(x) = x – 1 and g(x) = |x – 6| find the domain of the quotient function?
7. (5 pts) For income x (in dollars), a particular state's income tax T (in dollars) is given by
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0.025x if 0 < x < 2500 |
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T(x) = |
50 + 0.28(x – 2500) if 2500 < x < 10000 |
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250 + 0.04(x – 10000) if x >10000 |
(a) What is the tax on an income of $8,000?
(b) What is the tax on an income of $80,000?
8. (10 pts) Let y = 1 3x2.
(a) Find the x-intercept(s) of the graph of the equation, if any exist, and write as ordered pairs.
(b) Find the y-intercept(s) of the graph of the equation, if any exist, and write as ordered pairs.
(c) Create a table of sample points on the graph of the equation (include at least six points), and create a graph of the equation. (You may use the grid shown below, hand-draw and scan, or you may use the free Desmos graphing calculator described under Course Resource to generate a graph, save as a jpg and attach.)
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(x, y) |
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(d) Is the graph symmetric with respect to the y-axis? _____ (yes or no). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook.
(e) Is the graph symmetric with respect to the x-axis? _____ (yes or no). If no, state a point on the graph and state the appropriate reflection point which 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 origin? _____ (yes or no). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook.
9. (5 pts) Let f (x) = 2x2 + 4x – 6 and g(x) = 1 – x.
(a) Find (g – f)(–1) Show work.
(b) Find (f g)( –3) Show work.
(c) Find (f – g)(x + 3) and simplify the results. Show work.
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