## (Solved) College Algebra MATH 107 Spring, 2017, V.10 MATH 107 FINAL EXAMINATION This is an open-book exam. You may refer to your text and other course...

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College Algebra MATH 107 Spring, 2017, V.1.10 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.
There are 30 problems.
Problems #1â€“12 are Multiple Choice.
Problems #13â€“21 are Short Answer. (Work not required to be shown)
Problems #22â€“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 2 4 -2
-4
A.
B.
C.
D. Domain [0, 4]; Range [â€“ 4, 0]
Domain [â€“2, 0]; Range [0, 2]
Domain [0, 2]; Range [2, 4]
Domain [â€“ 4, 0]; Range [0, 4] 2. Solve:
A.
B.
C.
D. x + 17 = x âˆ’ 3 2. ______ No solution
âˆ’1
âˆ’1, 8
8 Page 1 of 11 College Algebra MATH 107 3. Determine the interval(s) on which the function is increasing. A. (â€“ 4, 2) B. (â€“1, 3) C. (â€“âˆž, â€“ 4) and (2, âˆž) D. (â€“6.7, 0) and (3.6, âˆž) Spring, 2017, V.1.10 3. ______ 4. Determine whether the graph of y = x + 8 is symmetric with respect to the origin,
the x-axis, or the y-axis.
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 â€“ 4x | â‰¥ 7.
A.
B.
C.
D. 5. ______ (â€“âˆž,3] âˆª [â€“1/2, âˆž)
(â€“âˆž, â€“1/2] âˆª [3, âˆž)
[â€“ 1/2, âˆž)
[â€“ 1/2, 3] Page 2 of 11 College Algebra MATH 107 Spring, 2017, V.1.10 6. Which of the following represents the graph of 3x âˆ’ 8y = 24 ?
A. B. C. D. 6. ______ Page 3 of 11 College Algebra MATH 107 Spring, 2017, V.1.10 7. Write a slope-intercept equation for a line parallel to the line x â€“ 8y = 3 which passes through
the point (16, â€“5).
7. ______
A. y = âˆ’8 x + 123 B. y= 1
xâˆ’7
8 C. y= 1
xâˆ’5
8 D. 1
y = âˆ’ x âˆ’3
8 8. Does the graph below represent a function and is it one-to-one? A.
B.
C.
D. 8. ______ It is a function and it is one-to-one.
It is a function but not one-to-one.
It is not a function but it is one-to-one.
It is not a function and it is not one-to-one. Page 4 of 11 College Algebra MATH 107 9. Express as a single logarithm: log x â€“ 3 log y + log 1
A. log ( x âˆ’ 3 y + 1) B. x +1 log y C. x log 3 y D. x log 3y +1 Spring, 2017, V.1.10 9. ______ 3 10. Which of the functions corresponds to the graph? 10. ______ A. f ( x ) = âˆ’e x + 3
B. f ( x ) = eâˆ’ x + 3
C. f ( x ) = eâˆ’ x + 4
D. f ( x ) = e x + 4 Page 5 of 11 College Algebra MATH 107 Spring, 2017, V.1.10 11. Suppose that for a function f , the equation f (x) = 0 has exactly one real-number solution.
Which of the following statements MUST be true?
A.
B.
C.
D. 11. ______ f (x) â‰¥ 0 for all x in the domain of f.
f is an invertible function.
f has exactly one x-intercept.
f is a linear function. 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. ______ -4 4 4 2 2
2 -2 4 -4 2 -2 -2 -2 -4 -4 y = f (x) y = g(x)
A.
B.
C.
D. 4 g(x) = f (x + 2) + 1
g(x) = f (x â€“ 2) â€“ 1
g(x) = f (x â€“ 1) + 2
g(x) = f (x â€“ 2) + 1 Page 6 of 11 College Algebra MATH 107 Spring, 2017, V.1.10 SHORT ANSWER:
13. Multiply and simplify: (8 + 5i)(1 + 2i).
Write the answer in the form a + bi, where a and b are real numbers. 14. Solve, and write the answer in interval notation: x +1
â‰¥0.
xâˆ’6 Answer: ________ Answer: ________ 15. A can of soda at 78Â° F. is placed in a refrigerator that maintains a constant temperature of 35Â°
F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by T(t) = 35 + 43e â€“ 0.058 t Find the temperature of the soda 20 minutes after it is placed in the refrigerator. (Round to the
nearest tenth of a degree.) Answer: ________ 1
16. Find the value of the logarithm: log 2 .
8 17. Solve: 95 x+7 = 81. Answer: ________ Answer: ________ 18. Suppose \$7,300 is invested in an account at an annual interest rate of 4.3% compounded
continuously. How long (to the nearest tenth of a year) will it take the investment to double in
size?
2 19. Let f (x) = x âˆ’ 6x + 2.
(a) Find the vertex. Answer: ________ (b) State the range of the function. Answer: ________ (c) On what interval is the function decreasing? Answer: ________ Page 7 of 11 College Algebra MATH 107 Spring, 2017, V.1.10 20. Consider the polynomial P(x), shown in both standard form and factored form.
1
1
7
1
1
P ( x) = x 4 + x 3 âˆ’ x 2 âˆ’ x + 3 = ( x + 3)( x + 1)( x âˆ’ 1)( x âˆ’ 2)
2
2
2
2
2
(a) Which sketch illustrates the end behavior of the polynomial function? B. A.
vvvv C.
vvvv D.
vvvv
vvvv Answer: ________ (b) State the y-intercept. Answer: ________________ (c) State the zeros of the function. Answer: ________________
Answer: ________ (d) State which graph below is the graph of P(x). GRAPH A GRAPH B GRAPH C GRAPH D Page 8 of 11 College Algebra MATH 107 21. Let f ( x) = Spring, 2017, V.1.10 3x 2 + 3
.
x2 âˆ’ 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 f ( x) = 3x 2 + 3
?
x2 âˆ’ 4 GRAPH A. GRAPH B. GRAPH C. GRAPH D. Answer: ______________ Page 9 of 11 College Algebra MATH 107 Spring, 2017, V.1.10 SHORT ANSWER, with work required to be shown, as indicated.
22. Let f (x) = x + 2 and g ( x) = 5 âˆ’ x .
f (a) Find (âˆ’4) . Show work.
g
(b) Find the domain of the quotient function f
. Explain.
g 23. Points (7, â€“3) and (9, â€“5) 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 (â€“1, 4) and (1, 8) . Write the
equation in slope-intercept form. Show work. 25. Adam, a resident of Metropolis, pays Metropolis an annual tax of \$32 plus 2.6% of his
annual income. If Adam paid \$1,670 in tax, what was Adamâ€™s income? Show work.
2 26. Let f (x) = 8x â€“ 2 and g(x) = x â€“ 4.
(a) Find the composite function ( f o g )( x) and simplify. Show work.
(b) Find ( f o g ) (3) . Show work. 2 27. Find the exact solutions and simplify as much as possible: 2x + 11 = 10x. Show work. 28. Given the function f ( x) = 1
x âˆ’ 7 , find a formula for the inverse function. Show work.
3 Page 10 of 11 College Algebra MATH 107 Spring, 2017, V.1.10 29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P, in
dollars, is given by P(x) = â€“0.002 x2 + 4.6x â€“ 1600
(a) What is the companyâ€™s profit if 600 donuts are made daily? (b) How many donuts should be made daily in order to maximize the companyâ€™s profit? Show
work. 30. Solve: x+9
28
+ 2
= 0 . Show work.
x + 7 x âˆ’ 49 Page 11 of 11

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