math107 final exam 2015 A+ answers

College Algebra MATH 107 Spring, 2015, V1.8

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.

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

There are 30 problems.

Problems #1–12 are Multiple Choice.

Problems #13–21 are Short Answer. (Work not required to be shown)

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. ______

4

2

-2 -4

A. Domain [1/2, 3/2]; Range [0, 1]

B. Domain [–3, 1]; Range [–1, 3]

C. Domain [–1, 1]; Range [0, 1]

D. Domain [–1, 3]; Range [–3, 1]

2. Solve:x+17=x?3 2. ______

A. No solution

B. 8

C. ?1, 8

D. ?1

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College Algebra MATH 107 Spring, 2015, V1.8

3. Determine the interval(s) on which the function is increasing. 3. ______

A. (–?, 3)

B. (– 2, 2)

C. (– 1, 3)

D. (–?, – 2.5) and (1, 4.5)

A. not symmetric with respect to thex-axis, not symmetric with respect to they-axis, and not symmetric with respect to the origin

B. symmetric with respect to thex-axis only

C. symmetric with respect to they-axis only

D. symmetric with respect to the origin only

5. Solve, and express the answer in interval notation: | 8 – 7x|?6. 5. ______

A. (–?, 2/7]

B. [2/7, 2]

C. (–?, 2]? [2/7,?)

D. (–?, 2/7]? [2,?)

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College Algebra MATH 107 Spring, 2015, V1.8

6. Which of the following represents the graph of 2x+ 9y= 18 ? 6. ______

A. B.

C. D.

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College Algebra MATH 107 Spring, 2015, V1.8

7. Write a slope-intercept equation for a line parallel to the linex– 8y= 16 which passes through the point (24, –1). 7. ______

A.y=¹x?4

8

B.y=¹x?1

8

C.y=?¹x?2

8

D.y=?2x+47

8. Which of the following best describes the graph? 8. ______

A. It is the graph of an absolute value relation.

B. It is not the graph of a function .

C. It is the graph of a function and it is one-to-one.

D. It is the graph of a function but not one-to-one.

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x⁹

C.y+3

D. log(9x?y? 2)^log

10. Which of the functions corresponds to the graph? 10. ______

A.f(x)=e^x+3

B.f(x)=e^?x+2

C.f(x)=e^?x+3

D.f(x)=?e^x+3

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College Algebra MATH 107 Spring, 2015, V1.8

11. The percentage score on a test varies directly as the number of correct responses. Paul answered 48 questions correctly and earned a score of 60%. What would Paul’s percentage score have been if he had answered 76 questions correctly? 11. ______

A. 61%

B. 63%

C. 88%

D. 95%

12. The graph ofy= formulas are given.)

f(x) is shown at the left and the graph ofy=g(x) is shown at the right. (NoWhat is the relationship betweeng(x) andf(x)?

12. ______

A.g(x) =f(x– 1) + 3

B.g(x) =f(x+ 1) – 3

C.g(x) =f(x+ 3) – 1

D.g(x) =f(x– 3) + 1

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15. A can of soda at 90° F. is placed in a refrigerator that maintains a constant temperature of 36° F. The temperatureTof the sodatminutes after it is placed in the refrigerator is given by

T(t) = 36 + 54e^{– 0.058t}

Find the temperature of the soda 12 minutes after it is placed in the refrigerator.(Round to the

nearest degree.)

Answer: ________

continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer: ________

19. Letf(x) =x²+12x+41.

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

GRAPH C GRAPH D

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College Algebra MATH 107 Spring, 2015, V1.8

21. Letf(x)=^2x?4.

GRAPH C. GRAPH D.

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College Algebra MATH 107 Spring, 2015, V1.8

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

(?2a⁶b⁵)³a⁷b^?8

23. Points (5, –2) and (9, –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 of the circle?

(c) What is the equation of the circle?

24. Find the equation for a line which passes through the points (7, 8) and (9, –2). Write the equation in slope-intercept form.Show work.

25. A salesperson earns a base salary of $1,900 per month and a commission of 7.3% on the amount of sales made. If the salesperson has a paycheck of $3,768.80 for one month, what was the amount of sales for the month?Show work.

26. Letf(x) = 3x²– 7 andg(x) =x– 6.

(a) Find the composite function (f g)(x) and simplify.Show work.

(b) Find(f g) (2) .Show work.

27. Find the exact solutions and simplify as much as possible: 2x²+ 5 = 2x.Show work.

28. Given the functionf(x)=⁶?¹x, find a formula for the inverse function.Show work.

77

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College Algebra MATH 107 Spring, 2015, V1.8

29. Chocolate Confections, Inc. has determined that whenxchocolate cakes are made daily, the average cost per chocolate cake is given by

C(x) = 0.001x²– 0.11x+ 13.70

(a) What is the average cost per cake if 40 chocolate cakes are made daily?

(b) How many chocolate cakes should be made daily in order to minimize the average cost per cake?Show work.

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