MATH 107 Problem solving paper

Instructions:

MATH 107 QUIZ 5 I Professor: Dr. Jill Whealon
I have completed this assignment myself, working independently and not consulting anyone except the instructor.
INSTRUCTIONS
· The quiz is worth 100 points. There are 8 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, just turn in your quiz before 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. (8 pts) Which of these graphs represent a one-to-one function? Answer(s): ____________
( no explanation required .) (There may be more than one graph that qualifies.)
(A) (B) (C) (D)
2. (8 pts) Based on data about the growth of a variety of ornamental cherry trees, the following logarithmic model about these trees was determined:
h(t) = 5.18 ln(t) + 8.199, where t = age of tree in years and h (t) = height of tree, in feet.
(Note that “ln” refers to the natural or base e log function)
Using the model, at age 4 years, how tall is this type of ornamental cherry tree, to the nearest tenth of a foot? Show your work.
3. (4 pts) Which response converts 9x = 729 to a logarithmic equation? (no explanation required) 2. ______
A. log9 729 = x
B. logx 729 = 9
C. logx 9 = 729
D. log9 x = 729
4. (16 pts) Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.
5. (12 pts)
(a) log4 1 = _______ (fill in the blank)
(b) Let State the exponential form of the equation.
(c) Determine the numerical value of in simplest form. Work optional.
6. (12 pts) Let f (x) = x2 – x – 7 and g(x) = 3x + 2
(a) Find the composite function and simplify the results. Show work.
(b) Find . Show work.
7. (20 pts) Let
(a) Find f 1 , the inverse function of f. Show work.
(b) What is the domain of f ? What is the domain of the inverse function f -1?
(c) What is f (2) ? f (2) = ______
(d) What is f 1 ( ____ ), where the number in the blank is your answer from part (c)? Show your work
8. (20 pts) Let f (x) = e x – 1 + 2.
Answers can be stated without additional work/explanation.
(a) Which describes how the graph of f can be obtained from the graph of y = ex ? Choice: ________
A. Shift the graph of y = ex to the left by 1 unit and up by 2 units.
B. Shift the graph of y = ex to the right by 1 unit and up by 2 units.
C. Reflect the graph of y = ex across the x-axis and shift up by 2 units.
D. Reflect the graph of y = ex across the y-axis and shift up by 2 units.
(b) What is the domain of f ?
(c) What is the range of f ?
(d) What is the horizontal asymptote?
(e) What is the y-intercept? State the approximation to 2 decimal places (i.e., the nearest hundredth).

RUBRIC
Excellent Quality 95-100%	Introduction 45-41 points The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.		Literature Support 91-84  points The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.			Methodology 58-53 points Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met.
Average Score 50-85%	40-38 points More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.		83-76  points Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.			52-49  points Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met.
Poor Quality 0-45%	37-1 points The background and/or significance are missing. No search history information is provided.		75-1 points Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration.			48-1 points There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met
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