MATH107 final exam 2016

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

-4 -2 2 4

-2 -4

A. Domain [–3, 3]; Range [–2, 4]

B. Domain [–3, 3]; Range [0, 3]

C. Domain [–2, 4]; Range [–3, 3]

D. Domain [–1, 4]; Range [–2, 2]

2. Solve: 2x+ 20= x+ 6 2. ______

A. ?8,?2

B. ?2

C. ?14

D. No solution

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College Algebra MATH 107 Spring, 2016, V1.7

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

A. (–3.6, 0) and (6.7,?)

B. (–2, 4)

C. (–?, –2) and (4,?)

D. (–1, 3)

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. 5. ______

A. [4/3,?)

B. (–?,?4/3]? [3,?)

C. (–?, 3]? [?4/3,?)

D. [–4/3, 3]

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College Algebra MATH 107 Spring, 2016, V1.7

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

A. B.

C. D.

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College Algebra MATH 107 Spring, 2016, V1.7

7. Write a slope-intercept equation for a line parallel to the line x + 3y = 8 which passes through the point (– 4, 5). 7. ______

A. y=?¹ x+¹¹

3 3

B. y=?¹ x+5

3

C. y=¹ x+5

3

D. y=?3x?7

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

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

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

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

D. It is not the graph of a function.

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

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

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

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

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

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College Algebra MATH 107 Spring, 2016, V1.7

11. Suppose that a function f has no x-intercepts.

Which of the following statements MUST be true? 11. ______

A. The graph of f has no points whose x-coordinate is 0.

B. The equation f (x) = 0 has no real-number solution.

C. f is an invertible function.

D. The graph of f is a horizontal line.

12. 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)?

12. ______

A.g(x) = f(x+ 2) + 4

B.g(x) = f(x+ 1) + 2

C.g(x) = f(x– 2) + 1

D.g(x) = f(x– 1) + 2

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15. A can of soda at 83° F. is placed in a refrigerator that maintains a constant temperature of 35° F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by

T(t) = 35 + 48 e^{– 0.058t}

Find the temperature of the soda 15 minutes after it is placed in the refrigerator.(Round to the

nearest tenth of a 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?10x+45.

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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, 2016, V1.7

GRAPH C. GRAPH D.

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College Algebra MATH 107 Spring, 2016, V1.7

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

(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 (–5, 6) and (–7, 8). Write the equation in slope-intercept form.Show work.

25. Elise, a resident of Metropolis, pays Metropolis an annual tax of $50 plus 1.6% of her annual income. If Elise paid $1,202 in tax, what was Elise’s income?Show work.

26. Letf(x) = 2x²– 9 and g(x) =x– 6.

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

(b) Find( f o g) (1) .Show work.

27. Find the exact solutions and simplify as much as possible: 5x²+ 1 = 8x.Show work.

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College Algebra MATH 107 Spring, 2016, V1.7

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+ 4.6x– 1600

(a) What is the company’s profit if 700 donuts are made daily?

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

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