MATH 107 Problem solving paper

MATH 107 Problem solving paper

Instructions/Descriptions

MATH 107 Problem solving paper

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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 bookand 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.)

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. ______
4. log9 729 = x
5. logx 729 = 9
6. logx 9 = 729
7. log9 x = 729
8. (16 pts) Solve the equation. Checkall proposed solutions. Show work in solving and in checking, and state your final conclusion.
9. (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) = ex– 1 + 2.

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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: ________

1. Shift the graph of y= ex to the left by 1 unit and up by 2 units.
2. Shift the graph of y= ex to the right by 1 unit and up by 2 units.
3. Reflect the graph of y= ex across the x-axis and shift up by 2 units.
4. 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).

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