Test Bank for College Algebra Final Exam and Review...Review Problem Set Revised Fall 2015 Page 1 Review for College Algebra Final Exam 1. Is r(t) a function? 10 a. r(t) is not a function

Review Problem Set Revised Fall 2015 Page 1

Review for College Algebra Final Exam 1. Is r(t) a function? a. r(t) is not a function b. r(t) is a function 2. Is r(t) a function?

t 1 3 4 5 r(t) 2 -1 2 3

a. r(t) is a function b. r(t) is not a function 3. Is r(t) a function? r(t) = {(-2, 1), (0, 3), (0, 4), (1, 0)} a. r(t) is a function b. r(t) is not a function

4. A store’s total sales, S, of a shirt when it is priced at price p, in dollars is giv

2 44.7S p= − + . Which of the following is the best interpretation of the slope of this function?

a. The sales are decreasing by two dollars per shirt. b. The sales are decreasing by two dollars per year. c. The sales are decreasing by two shirts per year. d. The sales are decreasing by two shirts per dollar. e. The sales are decreasing by two years per shirt.

5. Line l is given by

y = 3−23

x and point P has coordinates (6, 5). Find the equation of

the line containing P and perpendicular to l.

a.

y = −4 +32

x b.

y = 3 +32

x c.

y = 3 +65

x

d.

y = 3−32

x e.

y =14 +32

x

5 10-5-10

5

10

-5

-10

r(t)


6. Calculate the average rate of change between x = 4 and x = 8 for the function 3( ) 52

f x x= + .

a. 6 b. 92

c. 32

d. 4 e. 23

7. Find the average rate of change between the points (-2, f(-2)) and (3, f(3)) for the

function xxxf 22)( 2 −= a. 2 b. 1 c. 0 d. -2 e. 2 8. The population of a certain bacteria is growing exponentially according to the

function 100(1.035)tP = where t is the number of hours after 1pm. Find the average rate of change of the population from 3pm to 5pm. Round to the nearest tenth.

a.

bacteria7.6hour

b. bacteria3.8hour

c. bacteria7.1hour

d. bacteria11.6hour

e. none of these

9. The Robinson’s are planting a tree in their front yard. The sales person at the local

nursery tells them the tree they are purchasing will grow approximately half a foot every three years. The tree is four and one-half feet tall right now. Write an equation to model the height of this tree t years after it’s planted.

a.

h(t) = 4.5 + 0.167t b.

h(t) = 4.5 + 0.5t c.

h(t) = 412

+12

t

d.

h(t) = 5 + t e.

h(t) = 4.5 +t3

10. The table below gives data from a linear function. Find a formula for the function. Price per shirt, p($) 15 20 25 Number of shirts sold, q = f(p) 1000 750 500 a.

f ( p) = 1750p − 50 b.

f ( p) = 1000 − 50p c.

f ( p) = 1000 + 50 p d.

f ( p) = 1750 + 50 p e.

f ( p) = 1750 − 50p 11. Consider f(x) = 3x − 1. Find f(x + h) – f(x) and simplify. a. 3h b. h c. h − 2 d. 2x + 3h −1 e. fh − 2 12. Given 3)( 2 −= xxf find and simplify ( 2)f x + a. 12 +x b. 12 −x c. 22 −x d. 142 ++ xx e. 442 ++ xx 13. Given 3)( 2 −= xxf find and simplify ( ) 2f x + a. 12 +x b. 12 −x c. 22 −x d. 142 ++ xx e. 442 ++ xx


14. Given 3)( 2 −= xxf find and simplify ( ) ( )f a h f a+ − a. 22 hah + b. 62 2 −+ hah c. 2h d. 32 2 ++ hah e. 62 −h 15. Determine the range of the function:

y = −3x2 + 5 a. y > 5 b. y < 5 c. All real numbers d. y < 5 e. x < 5 16. Find the zeros of the function:

P( x) = x2 − 4x + 5. a. x = 0 b. x = −1, x = 5 c. x = 1, x = 5 d. x = 5 e. No real zeros

17. Find the domain of the function:

g( x) =x − 4x + 4

.

a. x ≠ −4 b. 4 < x < ∞ c. 4 < x < ∞ d. −4 < x < ∞ e. All real numbers 18. A cup of hot tea gradually cools off until it reaches room temperature. Sketch a graph

of the temperature of the tea vs time. a. b. c. d. e.

19. Consider the function given in the table:

x 0 1 2 3 4 5 F(x) 400 370 320 250 170 70

Which of the following best describe F(x): a. increasing, concave up b. decreasing, concave up c. increasing, concave down d. decreasing, concave down e. decreasing, no concavity

Temp

Time

Temp

Time

Temp

Time

Temp

Time

Time

Temp


20. Use function notation to write a formula for the function whose graph is shown below:

a.

f (x) =x + 2, 0 ≤ x ≤ 50, 5 < x ≤ 8

b. f(x) = x + 2

c.

f (x) =x + 2, 0 ≤ x ≤ 57, x ≥ 5

d.

f (x) =x + 2, 0 ≤ x ≤ 57, 5 < x ≤ 8

e.

Domain: 0 ≤ x ≤ 8Range: 2 ≤ f (x) ≤ 7

Questions 21 – 24 are based on the following: In 1980 the population of Chandler was 30,000. By 2003, it had grown to 170,000. 21. Assume that the growth was linear. On average, how many people were added to

Chandler’s population each year from 1980 to 2003? a. 140,000 people b. 6364 people per year c. 6087 people per year d. 67.4% per year e. 7391 people 22. Assuming that the growth was linear, give a formula that expresses the population x

years since 1980. a.

P = 30,000 + 6087x b.

P = 30,000 + 7391x c.

P = 30,000 + 6087 x d.

P = 30,000(1.0693) x e.

P = 6087x −12,022,174 23. Now, assume that the growth was exponential. What was the annual percent growth

rate? a. 7.83% per year b. 67.4% per year c. 1.0783% per year d. 6.087% per year e. 5.667% per year 24. Assuming that the growth was exponential, give a formula that expresses the

population x years since 1980. a.

P = 30,000(1.0693) x b.

P = 30,000 + 7391x c.

P = 30,000 + 6087 x d.

P = 30,000(1.0783) x e.

P = 4.22(1.0783) x

5 10

5

10y

x


25. What is the effective yield on an investment that pays 6.039% annual interest, compounded continuously

a. 6.2% b. 1.0603% c. 6.225% d. 6.039% e. Not enough info 26. What is the doubling time for an annual 5% growth rate? a. 14.2 years b. 5 years c. 13.9 years d. 33 years e. Not enough information given. 27. What is the doubling time for a quantity that triples every 5 years? a. 2.5 years b. 3.2 years c. 5 years d. 4 years e. Not enough information given. 28. What is the annual decay rate for a quantity that has a half life of 23 years? a. 3% b. 12% c. 5% d. 4% e. Not enough information given.

29. Use the properties of logs to expand:

logm2

n

a.

log2m − log n b.

(log m)2 − log n c.

2log m − log n

d.

2log mlog n

e.

m2

n

30. Solve for x:

ln x = 3 a. e b. 3e c. 3 d. ln(3) e. e3 31. Solve for a: 225loga = a. 2 b. 10 c. e d. 5 32. Solve for t: log (2t + 1 ) + 1 = 0

a. 10 b. 21 c.

21

− d. 2210 e.

209

−

33. Solve for x: 3)2(log)(log 22 =−+ xx a. 4 b. 2 c. -1 d. -2 e. no solution

34. If xb =2log and yb =3log find 8log27b in terms of x and y

a. 3x + 3y b. 3x – 3y c. x + y d. x – y e. none of these

35. Which of the following is NOT an equivalent way of writing 1lnxy

?

a. ( )ln xy− b. ( ) ( )ln lnx y− − c. ( ) ( )ln lnx y− + d. ( ) ( )( )ln lnx y− +


36. Find a quadratic equation, written in standard form, for the graph below:

a.

y = −12

x 2 + 2x + 2 b.

y = x 2 − 4x − 5 c.

y = x 2 + 4x +1

d.

y = −4x 2 + 2x + 2 e.

y = 4x2 + 2x + 2 37. The table displays ordered pairs for two functions, f and g. x –3 –2 –1 0 1 2 3

f (x ) 5 0 –3 –4 –3 0 5

g( x) –5 0 3 4 3 0 –5 Notice that g is a transformation of f. Describe specifically how g is related to f. a. f is not a function b. g is a reflection of f across the y-axis c. f and g are function inverses d. g is a shift of f down 5 units. e. g is a reflection of f across the x-axis Questions 38 – 39 are based on the following:

Let

f (x ) =13

x2 .

38. Describe in words the effects of the following transformation on the graph of

f (x ):

f (x + 3) + 9 a. The graph is moved 1 unit left and 3 units up. b. The graph is moved 3 units up and 9 units left. c. The graph is moved 3 units right and 9 units up. d. The graph is moved 3 units left and 9 units up. e. The graph is moved 1 unit right and 3 units down. 39. Write a formula for

y =

f (x + 3) + 9 .

a.

y = f (13

x 2 + 3) + 9 b.

y =13

(x + 3)2 + 9 c.

y =13

x 2 +12

d.

y = (x + 3)2 + 9 e.

y = (x +1)2 + 3


Questions 40 – 41 are based on the following:

x –3 –2 –1 0 1 2 3 G(x) 2 m 3 –2 5 H(x) 1 –7 4 0 n

40. Assuming that G(x) is an even function, what is the value of m? a. m = –5 b. m = 5 c. m = 1 d. m = 0 e. m = 2.5 41. Assuming that H(x) is an odd function, what is the value of n? a. n = –5 b. n = –7 c. n = 4 d. n = –2 e. n = 7 42. The figure below shows the graph of y = f(x). Which of the following is a graph of

y = −2 f (x)? a. b. c.

d. e.

1 2-1-2

1

2

-1

-2

(0.6, -0.4)

(-0.6, 0.4)

x

y


43. Which of the following is the range of f(x) = ln(x – 4)? a. x > 4.14 b. y > –1.9 c. y > 0 d. x > 0 e. all real numbers 44. Which of the following is an x-intercept of f(x) = ln(x – 4)? a. (0, 5) b. (–5, 0) c. (1, 0) d. No x-intercept e. (5, 0) 45. Which of the following is a y-intercept of f(x) = ln(x – 4)? a. (5, 0) b. (0, 1) c. (0, –4.14) d. (1, 0) e. no y-intercept 46. Which of the following is a vertical asymptote of f(x) = ln(x – 4)? a. x ≠ 4 b. x = 0 c. x = 4 d. y = 0 e. x = 5 47. If

f (x ) = 2x and

g( x) = x2 . Find

f (g(x )). Do not simplify. a.

f (g(x)) = f (2x2 ) b.

f (g(x)) = (2x)2 c.

f (g(x)) = 2x ⋅ x2 d.

f (g(x)) = 2x(x 2) e.

f (g(x)) = 2x2 For problems 48-50 use the following tables. Given that h(x) = f(g(x)), find the missing values

x f(x) x g(x) x h(x) 1 3 1 3 1 4 2 5 2 1 2 x 3 z 3 3 4 4 y 4 5 5 1 5 5

48. Find the value of x in the table. a. 1 b. 2 c. 3 d. 4 e. 5 49. Find the value of y in the table. a. 1 b. 2 c. 3 d. 4 e. 5 50. Find the value of z in the table a. 1 b. 2 c. 3 d. 4 e. 5

51. Let f(g(x)) =

41 + x2 . Which of the following are possible formulas for f(x) and g(x).

a.

f (x) =1 + x2 and g(x) =4x b.

f (x) =41

and g(x) =1

1+ x 2

c.

f (x) =4

1− x and g(x) = x2 d.

f (x) =4x

and g(x) = 1+ x 2

e.

f (x) = x 2 and g(x) =4

1− x


52. Which of the following methods would be inappropriate to show that

f (x ) = 3x + 2

and

g(x) =x − 2

3 are inverse functions of each other?

a. Compare the graphs of f(x) and g(x). b. Compare tables of values of f(x) and g(x). c. Show that f(x) and g(x) pass the horizontal line test. d. Find the inverse of f(x) algebraically. e. Show that f(g(x)) = g(f(x)) = x. Questions 53– 55 are based on the following: Let

f (x ) = x +1 and

g( x) = x2 +1. Write a formula for each function in terms of x. 53. h is the sum of f and g a.

(x +1) + (x2 +1) = 0 b.

h(x) = x2 + x +1 c.

h(x) = x3 + x +1 d.

h(x) = x3 + x 2 + x +1 e.

h(x) = x2 + x + 2 54. j is the product of f and g a.

j(x) = x3 + x 2 + x +1 b.

j(x) = x2 + x + 2

c.

j(x) = x3 + x +1 d.

j(x) =(x +1)(x2 +1)

e.

(x2 +1)(x +1) = 0 55. m is the square of f a.

m(x) = x +1 b.

m(x) = (x 2 +1)2 c.

(x2 +1)2 = (x +1)2 d.

x 2 +1= (x +1)2 e.

m(x) = (x +1)2

56. Newton’s Law of Gravitation states that the magnitude of the gravitational force, F, exerted by an object of mass M on an object of mass m is proportional to the product Mm and inversely proportional to the square of the distance d, between them. Write a formula for this law.

a. MmF kd

= b. 2F kMmd= c. 2

MmF kd

= d. M m

M mF kd d

−=

−

e. 2

1 MmF kd

=

57. State the range of

f (x ) = x4 − 4x2 + 2. a. –2 ≤ y < ∞ b. –2 < y < ∞ c. –2 < y < 10 d. –3 < x< 3 e. –∞ < y < ∞

1 2 3-1-2-3

5

10


58. State the domain of

r( x) =( x −1)( x − 2)

(x − 3) .

a. all reals b. all reals, x ≠ 3 c. all reals, x ≠ 1, x ≠ 3 d. –2 < y < ∞ e. –3 < x< 3 Questions 59– 61 are based on the following:

When a car skids to a stop, the length L, in feet, of the skid marks is related to the speed

S, in miles per hour, of the car by the power function

L =1

30hS2 . In this formula, h is a

constant that depends on the road surface (the friction coefficient). For dry concrete pavement, the value of h is about 0.85. 59. If a driver going 55 mph on dry concrete jams on the brakes and skids to a stop, how

long will the skid marks be? a. 4.65 feet b. 85.708 feet c. 1186 feet d. 118.6 feet e. 2.16 feet 60. A policeman investigating an accident on dry concrete pavement measures the skid

marks at 230 feet. How fast was the car going? a. 77 mph b. 90 mph c. 59 mph d. 81 mph e. Not enough information is given. 61. According to this formula, what is the effect of doubling your speed on the stopping

distance? a. Stopping distance is multiplied by

2 b. Stopping distance doubles c. Stopping distance is four times as great d. Stopping distance is cut in half e. Not enough information is given. Questions 62– 68 are based on the following: A partial graph of a polynomial y = p(x) is shown. The window is –7 < x <7, –4 < x <15. Answer True or False to each question: 62. One factor of p(x) is (x+5). a. True b. False 63. There is a double root at x = 0. a. True b. False 64. p(x) = p(–x). a. True b. False 65. p(0) = 0 a. True b. False 66. The highest power of p(x) could be 4. a. True b. False 67. The coefficient of the leading term is negative. a. True b. False 68. p(x) is an odd function. a. True b. False

1 2 3 4 5 6-1-2-3-4-5-6

5

10

15


69. Give a possible formula for the polynomial shown in the figure.

a. )3)(1)(3()( −++= xxxxxf b. )3)(1)(3()( 5

1 −++= xxxxxf

c. )3)(1)(3()( −++−= xxxxxf d. )3)(1)(3()( 51 −++−= xxxxxf

70. What is the least possible degree of the polynomial in number xxx? a. 2nd degree b. 3rd degree c. 4th degree d. 5th degree e. 6th degree 71. Suppose ( )f x is a polynomial function and r is a real number. Which of the

following statements is not( )f x

equivalent to the statement (x – r) is factor of the polynomial .

a. f(r) = 0. b. (r, 0) is an x-intercept of the graph. c. ( )0f = r.

d. x = r is a solution of the equation ( )f x = 0. e. r is the input and 0 is the output.

72. Construct a rational function

r( x) =p(x )q(x ) , having x = –2 and x = 3 as vertical

asymptotes and y = 4 as a horizontal asymptote. Both p(x) and q(x) are quadratic polynomials.

a.

r(x) =4x 2 + 3x − 5(x − 2)(x + 3)

b.

r(x) =4

(x + 2)(x − 3)

c.

r(x) =(x + 2)(x − 3)

4 d.

r(x) =4x 2 + 3x − 5(x + 2)(x − 3)

e.

r(x) =x 2 + 4

(x + 2)(x − 3)


Use the graph f(x) for problems 73-76

73. Write the equation(s) of the vertical asymptote(s) of f(x). a.

x = 0 b. 3,4 −== xx c. y = 0 d. 3,4 =−= xx e. there are none 74. If f(x) has a horizontal asymptote, write its equation. a. y = -2 b. y = 0 c. x = 0 d. y = 1 e. None 75. Determine the zero(s) of f(x).

a. x = –4, x = 3, x = 1 and x = –2 b. x = 4 and x = –3 c. x = 3 and x= - 4 d. x = -2 e. No zeros

76. Give a possible formula for f(x).

a.)4)(3(

2)(−+

−=

xxxxf b.

)4)(3(2)(

−++

=xx

xxf c. )4)(3(

2)(+−

−=

xxxxf

d. )4)(3(

2)(+−

+=

xxxxf e.

)4)(3(2)(

+++

=xx

xxf

Questions 77– 83 are based on the following: At time t months, t > 0, the population of Weezers is W(t) thousands, and the population of Zogs is Z(t) thousands. The formulas for these are given by

W( t ) = 1+10t 2

Z(t ) = (1.01) t

Answer True or False to each question: 77. The initial populations are the same. a. True b. False


78. After one month there are more Weezers than Zogs. a. True b. False 79. The Weezer population is growing at a decreasing rate. a. True b. False 80. The Zog population is growing at a decreasing rate. a. True b. False 81. There will always be more Weezers than Zogs. a. True b. False 82. In the long run there will be more Zogs than Weezers. a. True b. False 83. Z(t) is a power function. a. True b. False Questions 84 – 86 are based on the following: During an 18 month period, the price of a certain stock could be modeled by

P( t ) = 56.5(0.96) t , where t is the number of months since the start of the period.

84. The price of the stock during this period of time … a. decreased by 4% per month. b. decreased by 96% per month. c. decreased by 96¢ per month. d. Increased by 96% per month. e. doubled every 18 years.

85. What was the initial price of the stock? a. 54.25 b. 56.5 c. 58.85 d. 100 e. Not enough information is given.

86. What was the stock price at the end of the 18-month period? a. 53.14 b. 73.78 c. 27.01 d. 26.097 e. 27.10

87. Where is the x-intercept of the graph of

r( x) =m

( x − 3)+

n( x + 3) .

a. (m + n, 0) b. (0, 0) c. (3m – 3n , 0)

d.

3n − 3mm + n

,0

e. (m, –n)

88. For the linear function

y = 5x + 6 , when x increases by 10, how does y change? a. y increases by 56 b. y increases by 60 c. y increases by 50 d. It depends on how big x is e. y gets 10 times as big


89. For the exponential function

y = 200(2)x , when x increases by 3, how does y change? a. y increases by 1600 b. y becomes 8 times as big c. y becomes 3 times as big d. It depends on how big x is e. y doubles Questions 90 – 91 are based on the following: Biologists document that the larger the area of a region, the more species live there. The relationship is best modeled by a power function. Puerto Rico has 40 species of amphibians and reptiles on 3459 square miles and Hispaniola (Haiti and the Dominican Republic) has 84 species on 29,418 square miles. 90. Determine a power function that gives the number of species of amphibians and reptiles on a Caribbean island as a function of its area. a.

N(A) = 2.374(A)0.3466 b.

N(A) = 40(A)0.3466 c.

N(A) = 0.0017x + 34.137 d.

N(A) = 36.235(1.0000285)A e.

N(A) = 0.0000000787(A)6.643 91. Use the power function to predict the number of species of amphibians and reptiles on Cuba, which measures 44,218 square miles. a. 97 species b. 1630 species c. 109 species d. 128 species e. We don’t know how many species there are on Cuba. 92. Write the following sum in sigma notation: 2 – 10 + 50 – 250 + 1250 – 6250 + 31250

a. ( )7

1 1

1( 1) 2 5n n

n

− −

=

−∑ b. ( )7

1

15 2 n

n

−

=

−∑ c. ( )6

1

02 5n

n

−

=

−∑

d. ( )6

1

05 2n

n

−

=

−∑ e. ( ) ( )8

1 1

11 5 2n n

n

− −

=

−∑

93. Which of the following sequences is arithmetic?

a.1, 4, 9, 16, 25, 36… b.2, 4, 6, 8, 10, 12… c. 6

151

41

31

21 ,,,,

d.2, 8, 32, 128, 512… e.None of the above.

94. Find the annual percent growth rate of a quantity that doubles every 5 years. a. 20% b. 14.9% c. 10% d. 1.149% e. Not enough information given


95. The half-life of carbon-14 is approximately 5728 years. If a fossil is found with 10% of its initial amount of carbon-14 remaining, how old is it?

a. 125,182 years b. 19,028 years c. 871 years d. 573 years e. not enough info 96. A population of bacteria decays at a continuous rate of 10% per hour. If the

population starts out with 100,000 bacteria, how many bacteria would remain after 1 day (24 hours)?

a. 9,072 bacteria b. 7,977 bacteria c. 90,000 bacteria d. 10,000 bacteria 97. A population of bacteria is measured to be at 1,000 after 10 minutes since it appeared.

25 minutes after it appeared, it is measured to be 10,000. How many bacteria would there be after 50 minutes?

a. 100,000 b. 25,000 c. 464,000 d. 2.1 million e. 21.5 million 98. Sam walks for 5 hours along a straight path. During the first 3 hours, he walked at an

average rate of 5 mph. During the next 2 hours, he walked at an average rate of 3 mph. The table shows the data for this story.

h (hours) 0 1 2 3 4 5 m (miles) 0 5 10 15 18 21

Which formula expresses the distance that Sam walks as a function of time.

a. 4.26 0.86m h= + b. 5 , 0 33 6, 3 5h h

mh h

< ≤= + < ≤

c. 5, 0 33, 3 5

hm

h< ≤

= < ≤ d.

5.371 0.5714, 0 33.5 1.5, 3 5

h hm

h h+ < ≤

= − < ≤

e. 5 , 0 33 , 3 5h h

mh h

< ≤= < ≤

Use the following information in problems 99 and 100. Suppose the public buys n gallons of gas when the price is p dollars per gallon. Thus, ( )G p n= . 99. What is the meaning of G(p)+60? a. At least 60 gallons of gas are bought. b. The total price plus 60 dollars. c. The price went up 60 cents per gallon. d. To the total number of gallons bought, add 60 more gallons. e. G(p) is an increasing function. 100. What is the meaning of G(2p)? a. The number of gallons sold when the price is cut in half. b. It costs twice as much for n gallons. c. The number of gallons sold when the price doubles. d. The total cost of the gas is cut in half. e. The price doubled.


Use the following information in problems 101 and 102. Suppose that the revenue for selling n computers is R dollars. Thus, ( )R f n= . 101. Which of the following best describes the meaning of )2( nf .

a. The number of computers doubled. b. The revenue for selling twice as many computers. c. The company’s revenue is twice as much if they sell n computers. d. The total revenue for selling n computers is cut in half. e. The total revenue for selling half as many computers.

102. Which of the following best describes the meaning of )(2 nf .

a. The number of computers doubled. b. The revenue for selling twice as many computers. c. The company’s revenue is twice as much if they sell n computers. d. The total revenue for selling n computers is cut in half. e. The total revenue for selling half as many computers.

Use the following information to answer questions 103 and 104. A company that produces microwaves finds that it costs $30 for each microwave they produce. They model their cost with the following function, C = f(n) where C is the cost in dollars and n is the number of microwaves. 103. In the context of this problem, explain the meaning of f(0) in practical terms. a. When 0 microwaves, they have a cost of $30. b. The total cost of producing the microwaves. c. They have no costs. d. When you spend 0 dollars, you haven’t produced any microwaves. e. The cost even if no microwaves are produced. 104. In the context of this problem, explain the meaning of f -1(5000) in practical terms. a. It would cost $5000 to produce microwaves. b. When 5000 microwaves are produced, it will cost $150,000 . c. You subtract 5000 from the number of microwaves, then divide by 30. d. f -1(5000) number of microwaves that can be produced for $5000. e. f -1(5000) is the cost of producing 5000 microwaves. Use the following information to answer questions 105 and 106. Let P(x) be the amount of profit a company earns for producing x units of an item. It costs the company $10.95 to produce each item and they retail for $29.99. They also have an overhead cost of $5,995. 105. In the context of this problem explain the meaning of P(0) in practical terms. a. The number of items produced when they have a profit of $0 b. When they sell no items, they make a profit of $5,995. c. How many items they need to produce to break even. d. When they sell no items, they make a profit of -$5,995.


106. In the context of this problem explain the meaning of 1(0)P− in practical terms. a. The number of items produced when they have a profit of $0 b. The reciprocal of the profit when they produce 0 items. c. The product of 0 and 1P− . d. The number of items they have not sold. Questions 107-109 are based on the following function:

)2)(1()3)(4(2)(

−−+−−

=xx

xxxR

107. Write the equation(s) of the vertical asymptote(s) of ( )R x . a.

x = 0 b. 3,4 −== xx c.

y = 0 d. 2,1 == xx e. 3,4 =−= xx 108. If R(x) has a horizontal asymptote, write its equation. a. y = -2 b. y = 0 c. x = 0 d. y = 1 e. None 109. Determine the zero(s) of R(x). a. x = 4, x = –3, x = 1 and x = 2 b. x = 4 and x = –3 c. x = 3 and x = - 4 d. x = 1 and x = 2 e. No zeros 110. If an account has an annual growth rate of 4.5%, what is the continuous growth rate. a. 1.045% b. 4.5% c. 4.4% d. 4.6% e. 0.45 111. A population of bacteria is growing exponentially. Initially (when t = 0) there are 1000

organisms present. After 1 hour, there are 2500. How many will be present after 4 hours. a. 7000 organisms b. 14,000 organisms c. 36,000 organisms d. 39,000 organisms e. 41,000 organisms 112.The following table shows a store’s total sales, S, of a shirt when it is priced at price

p, in dollars. p 10 11 12 13 14 15 S 25 23 20 18 17 15

Use the regression capabilities of your calculator to find a regression equation for S as a linear function of p.

a. 2 44.7S p= − + b. 2 44.7S p= − − c. 0.5 22.1S p= − +

d. 0.5 22.1S p= − − e. 69.2(.9) pS =


115. Given the function 𝑓(𝑥) = 3𝑥2 − 5𝑥 + 2, evaluate the difference quotient 𝑓(𝑥+ℎ)−𝑓(𝑥)

ℎ .

a. 6x + 3h -5 b. 3h-5 c.3ℎ

2+6𝑥ℎ−10𝑥−5ℎ+4ℎ

d. 3ℎ2−10𝑥−5ℎ+4

ℎ e. None of These

116. Solve the equation 2𝑥2 − 4𝑥 − 3 = 0. a. 2±√10

2 b. 1 ± √10 c. ± √10 d. 2±√2

2 e. None of These

113.The following data is best modeled by a polynomial. Which one of the following regression models best fit this data.

x 0 2 4 6 8 10 12 14 16 18 20 y 5 12 14 15 11 8 3 0 7 12 20

a. 0.07 9y x= + b.

20.06 1.1 12.53y x x= − + c. 3 20.03 0.71 4.79 5.11y x x x= − + + d. 3 20.03 0.71 4.79 5.11y x x x= − + − + e. 20.06 1.1 12.53y x x= − − +

114. A population grows exponentially as shown below. Which one of the following is the regression model for this data.

x 1 2 3 4 y 6.3 18.9 56.7 170.1

a. 6.3(3)xy = b. 2.1(3)xy = c. 3(2.1)xy = d. 6.3(2)xy =

e. None of these


117. The graph of the quadratic function 𝑔(𝑥) = 14𝑥2 − 6𝑥 − 9 is a parabola. Find the

vertex of that parabola. a. �− 3

4, −27964

� b. �34

, −85564

� c. (-12, 99) d. (12, -45) e. None of These 118. Determine if 𝑓(𝑥) = 𝑥4 − 𝑥2 − 3 is odd, even, or neither. a. odd b. even c. Neither 119. Determine if 𝑓(𝑥) = 1

2𝑥3 − 2𝑥 is odd, even, or neither.

a. odd b. even c. Neither 120. Determine all of the x-intercepts of 𝑓(𝑥) = 𝑥(𝑥 − 3)(𝑥 + 5) a. (3,0) and (5,0) b. (-3,0) and (-5,0) c. (3,0) and (-5,0) d. (-3,0) and (5,0) e. None of These 121. Describe the end behavior, or long run behavior, of 𝑓(𝑥) = 3(2)𝑥 − 10 a. As 𝑥 → −∞ ,𝑓(𝑥) → −10 ; as 𝑥 → ∞ ,𝑓(𝑥) → ∞ b. As 𝑥 → −∞ ,𝑓(𝑥) → −10 ; as 𝑥 → ∞ ,𝑓(𝑥) → −∞ c. As 𝑥 → −∞ ,𝑓(𝑥) → ∞ ; as 𝑥 → ∞ , 𝑓(𝑥) → ∞ d. As 𝑥 → −∞ ,𝑓(𝑥) → −∞ ; as 𝑥 → ∞ ,𝑓(𝑥) → ∞ e. None of These 122. Describe the end behavior, or long run behavior, of 𝑓(𝑥) = 𝑥5 − 3𝑥3 + 𝑥 + 2. a. As 𝑥 → −∞ ,𝑓(𝑥) → −∞ ; as 𝑥 → ∞ ,𝑓(𝑥) → −∞ b. As 𝑥 → −∞ ,𝑓(𝑥) → −∞ ; as 𝑥 → ∞ ,𝑓(𝑥) → ∞ c. As 𝑥 → −∞ ,𝑓(𝑥) → ∞ ; as 𝑥 → ∞ , 𝑓(𝑥) → −∞ d. As 𝑥 → −∞ ,𝑓(𝑥) → ∞ ; as 𝑥 → ∞ , 𝑓(𝑥) → ∞ e. None of These


123. Describe the end behavior, or long run behavior, of 𝑓(𝑥) = −2(𝑥 − 1)3(𝑥 + 2)2. a. As 𝑥 → −∞ ,𝑓(𝑥) → −∞ ; as 𝑥 → ∞ ,𝑓(𝑥) → −∞ b. As 𝑥 → −∞ ,𝑓(𝑥) → −∞ ; as 𝑥 → ∞ ,𝑓(𝑥) → ∞ c. As 𝑥 → −∞ ,𝑓(𝑥) → ∞ ; as 𝑥 → ∞ , 𝑓(𝑥) → −∞ d. As 𝑥 → −∞ ,𝑓(𝑥) → ∞ ; as 𝑥 → ∞ , 𝑓(𝑥) → ∞ e. None of These 124. Given the function 𝑓(𝑥) = 3𝑥 − 5, which one of the following is the formula for the inverse function f -1(x)? a. 𝑓−1(𝑥) = 1

5𝑥 + 3

5 b. 𝑓−1(𝑥) = 1

3𝑥 + 5

3 c. 𝑓−1(𝑥) = 1

3𝑥+5

d. 𝑓−1(𝑥) = 3𝑥 − 5 e. 𝑓−1(𝑥) = −3𝑥 + 5 125. Given H = f(t), where H is the height (in meters) of an object, and 't' is the time in seconds since it was launched. Interpret the mathematical statement 𝑓−1(10) = 16.

a. After 110

of a second, the object is 16 meters high.

b. After 10 seconds, the object is 116

of a meter high. c. After 10 seconds, the object is 16 meters high. d. After 16 seconds, the object is 10 meters high. e. None of These

126. Use the table provided to determine the average rate of temperature change from day 1 to day 3. d (days) 1 2 3 4 5 6 7 T(d) (Temperature ºF) 78 88 89 70 65 68 82

a. 0.18ºF /day b. 5.5ºF /day c. 0.18 days/ ºF d. 5.5 days/ ºF e. None of These


127. Below is a graph of the function f. Estimate the average rate of change of the function f from x = 0 to x = 1.

a. 1/3 b. 1 c. 3 d. 6 e. None of These 128. Cameron is a door to door vacuum salesmen. His weekly salary 𝑆(𝑣) is given by

the linear function 𝑆(𝑣) = 400 + 120𝑣 , where 𝑣 is the number of vacuums sold. Identify the slope,

and explain the meaning of the slope. a. Cameron sells 120 vacuums per week b. Cameron gets a salary of $120 per week c. Cameron's weekly salary increases by $120 every time he sells a vacuum d. Cameron has a base salary of $400 e. Cameron always sells at least 400 vacuums per week 129. Identify the domain of 𝑦 = log2(2𝑥 − 4) using interval notation. a. x < 2 b. x > 2 c. (0, ∞) d. (-∞, 2) e. (2, ∞) 130. Find the solution of the exponential equation 8(𝑒)𝑥 − 6 = 17 in terms of logarithms. a. log �23

8� b. ln �23

8� c. log(15) d. ln(15) e. None of These

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Test Bank for College Algebra Final Exam and Review...Review Problem Set Revised Fall 2015 Page 1 Review for College Algebra Final Exam 1. Is r(t) a function? 10 a. r(t) is not a function