Document 6534445

Exam
Name
_
Sample Example 2
MULTIPLE CHOICE, Choose the one alternative
that best completes the statement or answers the question,
Evaluate the function at the given value of the independent
1) f(x) =~;
A) 3
C) -3
variable and simplify,
1)
f(-2)
B) 1.73
D) not a real number
' d an d si
h diff erence quotIen
' t f(x + h)h - f(x) ' h ~ 0 f or th e grven
'
fu nc tiIOn,
FIn
sImp lify
I tel
2) f(x)
=
6x - 2
2)
B) 6 + 12(~- 2)
A)6
D)O
Solve,
3) A faucet is used to add water to a large bottle that already contained some water, After it has been
filling for 5 seconds, the gauge on the bottle indicates that it contains 13 ounces of water, After it
has been filling for 13 seconds, the gauge indicates the bottle contains 29 ounces of water. Let y be
the amount of water in the bottle x seconds after the faucet was turned on. Write a linear equation
that models the amount of water in the bottle in terms of x.
1
21
A) Y = 2x + 16
B) Y = 2x + 3
C) Y = 2'x + 2
D) Y = -2x + 23
Find an equation for the line with the given properties,
4) The solid line L contains the point (-1, 4) and is perpendicular
y = 2x. Give the equation of line L in slope-intercept form,
to the dotted line whose equation is
3)
4)
y
5
x
-5
A) Y - 4 =
C) y - 4
-
1
-(x + 1)
2
1
B) y=-x+-
2
1
2
= 2(x + 1)
D) y= --x+-
7
2
7
2
Begin by graphing the standard quadratic function f(x) = x2 , Then use transformations
function,
1
of this graph to graph the given
5) hex)
(x - 7)2 - 5
=
5)
A)
B)
, ,
x
, ,
D)
C)
, ,
x
Find the domain of the composite function fo g.
2
6) f(x) =--9'
x+
g(x) = x + 5
6)
A) (-00, -14) or (-14,00)
C) (-00, -9) or (-9,00)
Find functions f and g so that h(x) =
7) h(x)=--
B) (-00, -9) or (-9, -5) or (-5,00)
D) (-00, 00)
(f
0
g)(x).
1
7)
_
x2 - 4
A) f(x) = l/x, g(x) = x2 - 4
B) f(x) = 1/4, g(x) = x2 - 4
C) f(x) = 1/x2, g(x) = x - 4
D) f(x) = 1/x2, g(x) = - 1/4
Graph f as a solid line and f-l as a dashed line in the same rectangular coordinate space. Use interval notation to give the
domain and range of f and f-l.
2
8) £(x)
= x3
8)
- 6
l-Bt-+HJ--t--"tH--++-++H+H+H---i
x
A)
B)
...... -- .. ------
1fH-~~~4t+-=P-+-+-HI~---.l--+--.!i-+--R--+---i
I
II
I
r
j domain = (-co, co); range = (-co, co)
j-l domain = (-co, co); range = (-co, co)
j domain
=
j-l domain
(0, co); range
= (-6,
=
(-6, co)
co); range
= (0, co)
D)
C)
1
- If.",H--:!.,. R--t'-'=!';--r-,#-t-=lZ-+--t----hI'!-t-4-~r+--R--+--1 x
I
II
r
I.
,
j domain = (-co, co); range = (-co, co)
j-l domain = (-co, co); range = (-co, co)
j domain = (- co, co); range = (- co, co)
j-l domain = (-co, co); range = (-co, co)
3
x
_
Find the midpoint of the line segment whose end points are given.
8 8
9) (-3'3)and(-2,1)
1
B) (_ ~, 16 )
A) (_ ~, ~)
Complete the square and write the equation in standard
10) x2 - lOx + 25 + y2 - 4y + 4
9)
C) (_ ~4, ~1)
form. Then give the center and radius of the circle.
= 36
10)
A) (x - 5)2 + (y - 2)2
(-5, -2), r = 36
= 36
B) (x - 2)2 + (y - 5)2
(2,5), r = 6
= 36
C) (x - 5)2 + (y - 2)2
(5,2), r = 6
= 36
D) (x - 2)2 + (y - 5)2
(-2, -5), r = 36
= 36
Solve the problem.
11) You have 120 feet of fencing to enclose a rectangular plot that borders on a river. If you do not
fence the side along the river, find the length and width of the plot that will maximize the area.
A) length: 60 feet, width: 60 feet
B) length: 90 feet, width: 30 feet
C) length: 60 feet, width: 30 feet
D) length: 30 feet, width: 30 feet
Find the zeros for the polynomial function and give the multiplicity
x-axis or touches the x-axis and turns around, at each zero.
12) f(x) = x3 + x2 - 6x
11)
for each zero. State whether the graph crosses the
12)
A) 0, multiplicity 1, touches the x-axis and turns around;
- 3, multiplicity 1, touches the x-axis and turns around;
2, multiplicity 1, touches the x-axis and turns around
B) 0, multiplicity 1, crosses the x-axis
3, multiplicity 1, crosses the x-axis
-2, multiplicity 1, crosses the x-axis
C) - 3, multiplicity 2, touches the x-axis and turns around
2, multiplicity 1, crosses the x-axis
D) 0, multiplicity 1, crosses the x-axis
- 3, multiplicity 1, crosses the x-axis
2, multiplicity 1, crosses the x-axis
Determine the maximum possible number of turning points for the graph of the function.
13) f(x) = (x - 5)(x - 2)(6x - 5)
A)3
B)2
C)6
D)O
13)
Solve the problem.
14) Use synthetic division to divide f(x) = x3 + 1x2 - 26x + 24 by x + 6. Use the result to find all zeros of
f.
B){6, 4, I}
C) (-6, 4, I}
A) (6, -4, -I}
D) (-6, -4, -I}
Find an nth degree polynomial function with real coefficients
15) n = 3; 3 and i are zeros; f(2) = 10
A) f(x) = 2x3 - 6x2 + 2x - 6
satisfying
14)
the given conditions.
15)
C) f(x) = 2x3 - 6x2 - 2x + 6
4
---
B) f(x)
=
-2x3 + 6x2 + 2x - 6
D) f(x)
=
-2x3 + 6x2 - 2x + 6
---
_
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function.
16) f(x) = -7x9 + x5 - x2 + 2
16)
A) 2 or 0 positive zeros, 3 or 1 negative zeros
B) 3 or 1 positive zeros, 3 or 1 negative zeros
C) 2 or 0 positive zeros, 2 or 0 negative zeros
D) 3 or 1 positive zeros, 2 or 0 negative zeros
Find the slant asymptote, if any, of the graph of the rational function.
17) f(x) = x2 + 5x - 5
x-4
17)
A) Y = x + 5
C) y = x + 9
B) Y = x
D) no slant asymptote
Solve the problem.
18) A company that produces radios has costs given by the function C(x) = 15x + 25,000, where x is the
number of radios manufactured and C(x) is measured in dollars. The average cost to manufacture
each radio is given by
C: (x) =
18)
15x + 25,000.
x
What is the horizontal asymptote for the function C? Describe what this means in practical terms.
A) y = 25,000; $25,000 is the least possible cost for running the company.
B) y = 15; 15 is the minimum number of radios the company can produce.
C) y = 15; $15 is the least possible cost for producing each radio.
D) y =25,000; 25,000 is the maximum number of radios the company can produce.
19) An arrow is fired straight up from the ground with an initial velocity of 240 feet per second. Its
height, s(t), in feet at any time t is given by the function s(t) = -16t2 + 240t. Find the interval of time
19)
for which the height of the arrow is greater than 576 feet.
A) after 3 sec
B) before 3 sec or after 12 see
C) before 12 sec
D) between 3 and 12 see
20) The amount of simple interest earned on an investment over a fixed amount of time is jointly
proportional to the principle invested and the interest rate. A principle investment of $2600.00 with
an interest rate of 8% earned $416.00 in simple interest. Find the amount of simple interest earned if
the principle is $1100.00 and the interest rate is 6%.
A) $13,200.00
B) $176.00
C) $132.00
D) $312.00
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20)
Answer Key
Testname: MATH 1314 COLLEGE ALGEBRA - SAMPLE EXAM 2
1) A
2) A
3) B
4) 0
5) A
6) A
7) A
8) C
9) B
10) C
11) C
12)0
13) B
14) C
15) 0
16) 0
17) C
18) C
19) 0
20) C
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