MULTIPLE CHOICE . Choose the one alternative that best
completes the statement or answers the question.
Simplify the difference quotient for the given function.
1) f(x) = -3x + 6 + x^2
A) -3a + h + 6
B) -3 + a^2 + 2a + h
C) -3a + 2ah + h
D) -3 + 2a + h
Solve the problem.
2) The median age of men at their first marriage has risen s lowly since 1980 and
can be modeled by
y = 24.8 + 0.13x, where x is the number of years after 1980. Inter pret the slope
of the equation .
A) The median age of men at their first marriage was 24.8 years in 1980.
B) The median age of men at their first marriage increases by 24.8 years per
year for each year
after 1980.
C) The median age of men at their first marriage increases by 0.13 year per year
for each year
after 1980.
D) The median age of men at their first marriage decreases by 0.13 year per year
for each year
after 1980.
3) The scores of students on a test can be modeled by the
equation y = 23.2 + 2.3x, where x is the
number of hours spent studying for the test. Interpret the slope of the
equation.
A) A student who doesn't study for the test can expect to score 23.2.
B) Test scores increase by 23.2 for each hour spent studying for the test.
C) A student who doesn't study for the test can expect to score 2.3.
D) Test scores increase by 2.3 for each hour spent studying for the test.
4) Market supply and demand, in hundreds, for DVD players
is given by S(x) = 5x - 4.5 and
D(x) = 13.5 - 3x, where x is the price per DVD player. Find the equilibrium
value and interpret its
meaning.
A) Supply equals demand if the price per DVD player is $3.25.
B) Supply equals demand if the price per DVD player is $2.25.
C) The company will break even if the price per DVD player is $2.25.
D) The company will break even if the price per DVD player is $3.25.
5) A manufacturer de termines that its profit, in dollars,
can be modeled by P = 2n^2 - 10n - 165,
where n is the number of units manufactured Given that the profit was $435, how
many units
were manufactured?
A) 25 units
B) 15 units
C) 30 units
D) 20 units
6) Suppose the cost of producing x items is given by C(x)
= 5600 - x^3 and the revenue made on the
sale of x items is R(x) = 400x - 14x^2. Find the number of items that should be
produced and sold
in order to break even.
A) 14 items
B) 49 items
C) 7 items
D) 140 items
7) John owns a hotdog stand. He has found that his profit
can be modeled by the equation
P(x) = -x^2 + 12x + 42, where x is the number of hotdogs sold. What is his
maximum profit?
A) $12
B) $21
C) $42
D) $78
8) A manufacturer determines its daily cost to be C(x) =
8x + 5 and its daily revenue to be
R(x) = 20x - 0.5x^2, where x is the number of units manufactured each day.
Determine the number
of units that should be manufactured daily to maximize profit.
A) 17 units
B) 12 units
C) 28 units
D) 13 units
Find the equilibrium point for the supply and demand
curves . Round answers to two decimal places.
9) D(p) = 10,500 - 25p, S(p) = 7200 + 5p
A) (110.00, 7750)
B) (590.00, -4250)
C) (165.00, 6375)
D) (-165.00, 14,625)
Use the ZERO or the INTERSECT feature on your calculator
to approximate all the zeros of the function to three
decimal places .
10) f(x) = 0.9x^3 - 5x^2 + 6x + 1.23 10)
A) -0.178, 2.137
B) -0.251, -1.334, -4.045
C) -0.178, 2.137, 3.596
D) -0.25, 2, 3.6
Determine what kind of function might be used as a model
for the data.
11)
A) Quadratic: f(x) = ax^2 + bx + c, a<0
B) Quadratic: f(x) = ax^2 + bx + c, a>0
C) Polynomial , but neither quadratic nor linear
D) Linear: f(x) = mx + b
Solve the problem.
12) The information in the chart below gives the salary of a person for the
stated years. Model the
data with a linear function using the points (1, 24,500) and (3, 26,700). Then
use this function to
predict the salary for the year 2002.
A) $36,700
B) $36,740
C) $36,720
D) $36,680
13) A furniture manufacturer decides to make a new line of
desks. The table shows the profit, in
thousands of dollars, for various levels of production.
Number of
Find a quadratic function to model the data, and use the model to predict the
profit if 450 desks are
made.
A) Just over $40,000
B) Almost $42,000
C) Just under $45,000
D) Almost $44,000
14) The following points form a quadratic relationship:
(1, 5.0), (2, 4.4), (3, 4.3), (4, 4.2), (5, 4.6), (6, 4.8),
(7, 5.4), (8, 6.2). The x- coordinates are the years a particular company has
been in operation and
the y -coordinates are the profit, in millions, for that year. Use quadratic
regression to estimate the
profit in the ninth year.
14)
A) 6.48 million
B) 7.19 million
C) 4.47 million
D) 7.38 million
15) Find the interest earned on $8000 invested for 7 years
at 6.5% interest compounded quarterly. 15)
A) $2025.31
B) $4563.35
C) $12,563.35
D) $1.57
Rewrite the expression as a sum , difference, or product of
simpler logarithms .
Find the domain of the function.
18) f(x) = ln (1 - x)
A) x > -1
B) x < -1
C) x > 1
D) x < 1
Find the asymptotes of the function.
19) 
A) Vertical asymptote at x = 9/4; horizontal asymptote at y = 9
B) Vertical asymptote at x = 0; horizontal asymptote at y = 9/4
C) Vertical asymptote at x = 9/4 horizontal asymptote at y = 0
D) Vertical asymptote at x = 9; horizontal asymptote at y = 9/4
20)
A) Vertical asymptote at x = 5; horizontal asymptote at y = 3
B) Vertical asymptote at x = - 1; horizontal asymptote at y = 5
C) Vertical asymptote at x = 5; horizontal asymptote at y = - 1
D) Vertical asymptote at x = 5; horizontal asymptote at y = 1
