Quiz08

College Algebra MATH 107 Fall 2020

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MATH 107 FINAL EXAMINATION

This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed. The exam starts at 12:01 on Sunday 10/11/2020 and must finish by 10/13/2020 11:59 P.M. Please use the answer sheet. Show your work, plot the graph using DESMOS or TI-calculator. Please do not submit any extra Excel or file.jpeg or file.png file. Thank you. Sincerely, Dr. K.S. Altmayer

Record your answers and work on the separate answer sheet provided.

There are 30 problems. Problems #1–11 are Multiple Choice. Problems #12–21 are Short Answer. (Show some) Problems #22–30 are Short Answer with work required to be shown.

MULTIPLE CHOICE

1. Determine the domain and range of the piecewise function. 1.

A. Domain [–1, 3]; Range [–3, 1] B. Domain [–1, 1]; Range [–1, 1] C. Domain [–3, 1]; Range [–1, 3] D. Domain [1/2, 3/2]; Range [0, 1]

2. Solve: = − x

2.

A. –8 B. –8, 3 C. 1/6 D. No solution

4 2

-4 -2 2 4 -2

-4

College Algebra MATH 107 Fall 2020

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3. Determine the interval(s) on which the function is decreasing. Show work. 3.

A. (–∞, – 4) and (1, ∞)

B. (– 4, –1.2)

C. (–∞, –2)

D. (– 5.5, –2)

4. Determine whether the graph of the x-axis, or the y-axis.

y = x − 4 is symmetric with respect to the origin,

4.

A. symmetric with respect to the x-axis only B. symmetric with respect to the y-axis only C. symmetric with respect to the origin only D. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and

not symmetric with respect to the origin

5. Solve, and express the answer in interval notation: | 5 – 6x | ≤ 13. Show work. 5.

A. (–∞, −4/3] ∪ [3, ∞) B. [3, ∞) C. [–3, 4/3] D. [–4/3, 3]

College Algebra MATH 107 Fall 2020

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6. Which of the following represents the graph of 4x − 9y = 36 ? Show work. 6.

A. B.

C. D.

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7. Write a slope-intercept equation for a line parallel to the line x – 4y = 6 which passes through the point (12, –3). Show work. 7.

A. y = − 4x + 45

B. y = 1 x − 3 4

C. y = 1 x − 6

4

D. y = − 1 x −1 4

E. None

8. Does the graph below represent a function and is it one-to-one? Show work. 8.

A. It is a function and it is one-to-one. B. It is not a function, but it is one-to-one. C. It is a function but not one-to-one. D. It is not a function and it is not one-to-one.

College Algebra MATH 107 Fall 2020

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9. Solve the equation for x using the One-to-One Property.

a. –11 b. 0 c. The equation has no solution. d. –9 e. 11

10. Which of the functions corresponds to the graph? Show work, attach screenshot

10.

a. f (x) = −ex + 2 b. f (x) = e−x + 2 c. f (x) = ex + 2 d. f (x) = e−x +1

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11. The graph of y = f (x) is shown at the left and the graph of y = g(x) is shown at the right. (No formulas are given.) What is the relationship between g(x) and f (x)? show work.

12.

y = f (x) y = g(x)

A. g(x) = f (x + 1) – 1 B. g(x) = f (x + 1) + 1 C. g(x) = f (x – 1) – 1 D. g(x) = f (x – 1) + 1

4 2

-4 -2 2 4 -2

-4

-4 -2 2 4 -2

-4

4

2

College Algebra MATH 107 Fall 2020

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SHORT ANSWER: Show some work and/or attach screenshot. 12. Multiply and simplify: (9 + i)2.

Write the answer in the form a + bi, where a and b are real numbers. Answer:

13. Solve, and write the answer in interval notation: x + 7

≥ 0 . Answer:

x −1

14. A bowl of soup at 170° F. is placed in a room of constant temperature of 60° F. The temperature T of the soup t minutes after it is placed in the room is given by

T(t) = 60 + 110 e – 0.075 t

Find the temperature of the soup 16 minutes after it is placed in the room. (Round to the nearest degree.)

Answer:

15. Solve: 44x− 9 =16. Answer:

16. Suppose $6,500 is invested in an account at an annual interest rate of 3.7% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer:

17. Determine the zeros (if any) of the rational function

.

a. b. no zeros c. d.

e.

Answer:

College Algebra MATH 107 Fall 2020

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18. Use the position equation to write a function that represents the situation and give the average velocity of the object from time t1 to time t2. An object is thrown upward from a height of 174 feet at a velocity of 1 feet per second. t1 = 1, t2 = 5 a. b. c. d. e.

19. Let f (x) = x2 − 12x + 28.

(a) Find the vertex.

(b) State the range of the function. Answer:

(c) On what interval is the function increasing? Answer:

College Algebra MATH 107 Fall 2020

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20. Consider the polynomial P(x), shown in both standard form and factored form.

P(x)= 1 10 𝑥𝑥4 − 1

2 𝑥𝑥3 − 7

10 𝑥𝑥2 + 41

10 𝑥𝑥 − 3 = 1

10 (𝑥𝑥 + 3)(𝑥𝑥 − 1)(𝑥𝑥 − 2)(𝑥𝑥 − 5)

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

Answer:

(b) State the zeros of the function. Answer:

(c) State the y-intercept. Answer:

(d) State which graph below is the graph of P(x). Answer:

GRAPH A GRAPH B

A. vvvv

B. vvvv

C. vvvv

D. vvvv

College Algebra MATH 107 Fall 2020

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GRAPH C GRAPH D

College Algebra MATH 107 Fall 2020

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21. Let

f (x) =

3x2 − 3 x2 − 4

.

(a) State the domain. Answer:

(b) State the vertical asymptote(s). Answer:

(c) State the horizontal asymptote. Answer:

(d) Which of the following represents the graph of the function f(x)=3𝑥𝑥

2−3 𝑥𝑥2−4

? Answer__________

Ans wer:

GRAPH A. GRAPH B.

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GRAPH C. GRAPH D.

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SHORT ANSWER, with work required to be shown, as indicated.

22. Use a graphing utility to graph the parabola. Plot the graph with all the axes and intersection points if any. Create a table for the values of x and y.

23. Points (–5, 2) and (–1, 8) are endpoints of the diameter of a circle.

(a) What is the length of the diameter? Give the exact answer, simplified as much as possible. Show work. (b) What is the center point C of the circle? (c) Given the point C you found in part (b), state the point symmetric to C about the y-axis.

24. Find the equation for a line which passes through the points (4, –3) and (6, –7). Write the equation in slope-intercept form. Show work and plot the graph.

25. A salesperson earns a base salary of $1,260 per month and a commission of 5.6% on the amount of sales made. If the salesperson has a paycheck of $3,959.20 for one month, what was the amount of sales for the month? Show work.

26. Let f (x) = 5x2 + 9 and g(x) = x + 3.

(a) Find the composite function ( f οg)(x) and simplify. Show work. (b) Find ( f o g )(−5) . Show work.

27. Find the exact solutions and simplify as much as possible: 8x2 + 11 = 20x. Show work.

28. Given the function f (x) = 7 + 1 x , find a formula for the inverse function. Show work. 2

College Algebra MATH 107 Fall 2020

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29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P (in dollars) is given by

P(x) = –0.002 x2 + 4.5x – 1700

(a) What is the company’s profit if 900 donuts are made daily?

(b) How many donuts should be made daily in order to maximize the company’s profit? Show work.

. . 30. Find a polynomial with real coefficients that has zeros –10, 2i, and –2i. a. b. c. d. e.