Week 8 - Math Quiz
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math107fall15c.pdf
College Algebra MATH 107 Fall, 2015, V4.6
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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. 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. ______ A. Domain [–1, 3]; Range [–1, 1] B. Domain [–1, 3]; Range [–2, 2] C. Domain [–2, 1/2]; Range [1/2, 3/2] D. Domain [–2, 2]; Range [–1, 3]
2. Solve: 3 5 3x x− = − 2. ______
A. No solution B. 2 C. 7 D. 2, 7
2 4 -4
-2
-4
2
4
-2
College Algebra MATH 107 Fall, 2015, V4.6
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3. Determine the interval(s) on which the function is decreasing. 3. ______
A. (–∞, –1)
B. (– 4.5, – 1) and (2.5, ∞) C. (– 2, 2)
D. (–∞, – 3) and (1, ∞)
4. Determine whether the graph of 5y x= − is symmetric with respect to the origin,
the x-axis, or the y-axis. 4. ______ A. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and not symmetric with respect to the origin B. symmetric with respect to the x-axis only C. symmetric with respect to the y-axis only D. symmetric with respect to the origin only
5. Solve, and express the answer in interval notation: | 9 – 6x | ≥ 3. 5. ______
A. (–∞, 2] ∪ [1, ∞)
B. (–∞, 1] ∪ [2, ∞)
C. [1, ∞) D. [1, 2]
College Algebra MATH 107 Fall, 2015, V4.6
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6. Which of the following represents the graph of 4x − 9y = 36 ? 6. ______ A. B.
C. D.
College Algebra MATH 107 Fall, 2015, V4.6
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7. Write a slope-intercept equation for a line parallel to the line x – 8y = 9 which passes through the point (16, –5). 7. ______
A. 1
3 8
y x= − −
B. 1
7 8
y x= −
C. 1
5 8
y x= −
D. 8 123y x= − +
8. Which of the following best describes the graph? 8. ______
A. It is not the graph of a function. B. It is the graph of an absolute value relation. 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.
College Algebra MATH 107 Fall, 2015, V4.6
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9. Express as an equivalent expression: log x + log 1 – 6 log (y + 4) 9. ______
A. 6
log ( 4)
x
y
+
B. 6
log
log( 4)
x
y +
C. ( )log 6 23x y− −
D. 1
log 6
x
y
+
10. Which of the functions corresponds to the graph? 10. ______
A. ( ) 3xf x e= − +
B. ( ) 2xf x e−= +
C. ( ) 2xf x e= +
D. ( ) 3xf x e= +
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11. Suppose that for a function f , the equation f (x) = 0 has no real-number solutions. Which of the following statements MUST be true? 11. ______ A. f (x) > 0 for all x in the domain of f. B. f is an invertible function. C. f has no x-intercepts. D. f has no y-intercepts. 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. ______ y = f (x) y = g(x) A. g(x) = f (x – 2) + 2 B. g(x) = f (x + 1) – 2 C. g(x) = f (x + 2) – 1 D. g(x) = f (x – 1) – 2
2 4 -2 -4
-2
-4
2
4 y = f(x)
2 4 -2 -4
-2
-4
2
4
College Algebra MATH 107 Fall, 2015, V4.6
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SHORT ANSWER: 13. Multiply and simplify: (4 + 9i)(3 + 2i). Write the answer in the form a + bi, where a and b are real numbers. Answer: ________
14. Solve, and write the answer in interval notation: 1
0 4
x
x
+ ≤
− . Answer: ________
15. A bowl of soup at 200° F. is placed in a room of constant temperature of 70° F. The temperature T of the soup t minutes after it is placed in the room is given by
T(t) = 70 + 130 e – 0.075 t
Find the temperature of the soup 8 minutes after it is placed in the room. (Round to the nearest degree.) Answer: ________
16. Find the value of the logarithm: 9 1
log 81
. Answer: ________
17. Solve: 6 15 25x − = . Answer: ________
18. Suppose $1,800 is invested in an account at an annual interest rate of 3.9% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer: ________
19. Let f (x) = x 2 + 8x + 7.
(a) Find the vertex. Answer: ________ (b) State the range of the function. Answer: ________ (c) On what interval is the function increasing? Answer: ________
College Algebra MATH 107 Fall, 2015, V4.6
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20. Consider the polynomial P(x), shown in both standard form and factored form.
3 21 3 13 1 ( ) 3 ( 3)( 1)( 5)
5 5 5 5 P x x x x x x x= − + + − = − + − −
(a) Which sketch illustrates the end behavior of the polynomial function?
Answer: ________
(b) State the y-intercept. Answer: ________________
(c) State the zeros of the function. Answer: ________________
(d) State which graph below is the graph of P(x). Answer: ________
GRAPH A GRAPH B
GRAPH C GRAPH D
A.
B. C. D.
vvvv
vvvv vvvv vvvv
College Algebra MATH 107 Fall, 2015, V4.6
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21. Let 3 9
( ) 2
x f x
x
− =
− .
(a) State the domain. Answer: _________________
(b) State the horizontal asymptote. Answer: _________________
(c) State the vertical asymptote(s). Answer: _________________
(d) Which of the following represents the graph of 3 9
( ) 2
x f x
x
− =
− ? Answer: ______________
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.
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SHORT ANSWER, with work required to be shown, as indicated.
22. Let 4)( −= xxf and g(x) = x − 8.
(a) Find )13(
g
f . Show work.
(b) Find the domain of the quotient function g
f . Explain.
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 (– 6, 3) and (– 4, –9). Write the equation in slope-intercept form. Show work.
25. Wanda, a resident of Metropolis, pays Metropolis an annual tax of $85 plus 1.6% of her annual income. If Wanda paid $693 in tax, what was Wanda’s income? Show work.
26. Let f (x) = 4x 2 + 9 and g(x) = x – 1.
(a) Find the composite function ))(( xgf o and simplify. Show work.
(b) Find ( ) )2(−gf o . Show work.
27. Find the exact solutions and simplify as much as possible: 2x 2 = 8x + 3. Show work.
28. Given the function 9 1
( ) 5 5
f x x= + , find a formula for the inverse function. Show work.
College Algebra MATH 107 Fall, 2015, V4.6
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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) = –0.001 x 2 + 1.9x – 350
(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? Show work.
30. Solve: 2
9 36 0
6 36
x
x x
+ + =
+ − . Show work.
