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MATH 107 QUIZ 5 November 9, 2015 Instructor: R. Smith

NAME: _______________________________

I have completed this assignment myself, working independently and not consulting anyone except the instructor.

INSTRUCTIONS

· The quiz is worth 100 points. There are 15 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, November 15.

· 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 Unit Quizzes module.

If you have any questions, please contact me by e-mail.

1. Find all of the zeros of the polynomial function and state the multiplicity of each. (no explanation required)

f (x) = (x2 − 36)2

A. with multiplicity 2 and with multiplicity 2

B. –6 with multiplicity 2 and 6 with multiplicity 2

C. 6 with multiplicity 4

D. –6i with multiplicity 2 and 6i with multiplicity 2

2. The function f (x) = 0.00303 x2 − 0.576x + 58 relates cholesterol level to heart attack rates for men. The variable x is the cholesterol level, and f (x) is the estimate of the number of men per 10,000 with cholesterol level of x who suffer a heart attack. Given a cholesterol level of 340, which of the following is the corresponding estimate for the number of men per 10,000 having a heart attack? (no explanation required)

A. 31

B. 212

C. 350

D. 604

3. For f (x) = x3 – 5x − 7, use the Intermediate Value Theorem to determine which interval must contain a zero of f(x). (no explanation required)

A. Between 0 and 1

B. Between 1 and 2

C. Between 2 and 3

D. Between 3 and 4

4. Solve the inequality x(x + 9)(x − 7) > 0 and express the solution set in interval notation. (no explanation required)

A. (–9, 0) (7,)

B. (–, –9) (0, 7)

C. (0,)

D. (7,)

5. Consider the following graph of a quadratic function y = f (x).

Which of the following is the solution set of the

inequality f (x) ≤ 0 ?

That is, for what x values is f (x) ≤ 0 ?

(no explanation required)

A. (–, –1]

B. (–, 0]

C. [–4, 0]

D. [–3, 1]

6. Let .

(a) State the domain.

(b) State the y-intercept.

(d) State the vertical asymptote(s).

(e) State the horizontal asymptote.

7. Let When factored,

(a) State the domain.

(b) Which sketch illustrates the end behavior of the polynomial function?

vvvv

Answer: ________

(d) State the x-intercepts:

(e) State which graph below is the graph of P(x).

GRAPH A. (below) GRAPH B. (below)

GRAPH C. (below) GRAPH D. (below)

8. Which of the following functions is represented by the graph shown below?

Explain your answer choice. Be sure to take the asymptotes and/or intercepts into account in your explanation.

9. Solve ≤ 0 and write interval notation for the solution set.

Show careful algebraic work/explanation.

10. Use composition of functions to show that the functions

and are inverse functions.

That is, carefully show that and show that .

11. Consider

a) Determine whether the function is one-to-one.

b) If it is one-to-one, find a formula for its inverse.

c) Graph the function and its inverse.

12. Convert to a logarithmic equation: 6x = 1296. (no explanation required)

13. Use a calculator (standard scientific calculator or an online graphing calculator) to find each of the following numerical values. Write your answer rounded to 4 decimal places (i.e., the nearest ten thousandth).

(a) 5 – 3.8

(b) e 0.76

14.

(a) _______ (fill in the blank)

For parts b and c, let .

(b) Write the exponential form of the equation.

15. (18 pts) Let f (x) = e – x + 3.

Answers can be stated without additional work/explanation.

(a) Which describes how the graph of f can be obtained from the graph of y = e x ? Choice: ___

A. Shift the graph of y = e x to the right by 1 unit and shift upward by 3 units.

B. Shift the graph of y = e x to the left by 1 unit and shift upward by 3 units.

C. Reflect the graph of y = e x across the x-axis and shift upward by 3 units.

D. Reflect the graph of y = e x across the y-axis and shift upward by 3 units.

(b) What is the y-intercept?

(d) What is the range of f ?

(f) Which is the graph of f ?

GRAPH A GRAPH B GRAPH C

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