A)
B)
C)
D)
Solve the equation.
177)
Solve for x: (ex)x·e24 =e10x
177)
A)
{4}
B)
{6, 4}
C)
{-6, -4}
D)
{6}
Give the domain and range of the function.
178)
s(x) =-6 – x
178)
A)
Domain: (–, -6) (-6, ); Range: (–, 0)
(0, )
B)
Domain: ( -6, ); Range: (–, 0]
C)
Domain: all real numbers; Range: [0, )
D)
Domain: (–, -6]; Range: [0, )
Solve the problem.
179)
The following table shows a recent state income tax schedule for married couples filing a joint
return in State X.
State X Income Tax
SCHEDULE I – MARRIED FILING JOINTLY
If taxable income is
Over But not over Tax due is
$0 $40,000 4.25% of taxable incomes
$40,000 $70,000 $3700 plus 6.75% of excess over $40,000
$70,000 $3875 plus 7.05% of excess over $70,000
(i) Write a piecewise definition for the tax due T(x) on an income of x dollars. (ii) Graph T(x). (iii)
Find the tax due on a taxable income of $50,000. Of $95,000.
179)
78
A)
(i)
T(x) =
0.0425x if 0
x
40,000
0.0675x – 990 if 40,000 < x
70,000
0.0705x – 1000 if x > 70,000
(ii)
(iii) $2385; $5697.50
B)
(i)
T(x) =
0.0425x if 0
x
40,000
0.0675x – 1025 if 40,000 < x
70,000
0.0705x – 1375 if x > 70,000
(ii)
(iii) $2350; $5322.50
79
C)
(i)
T(x) =
0.0425x if 0
x
40,000
0.0675x – 1000 if 40,000 < x
70,000
0.0705x – 1060 if x > 70,000
(ii)
(iii) $2375; $5637.50
D)
(i)
T(x) =
0.0425x if 0
x
40,000
0.0675x – 1300 if 40,000 < x
70,000
0.0705x – 1427 if x > 70,000
(ii)
(iii) $2075; $5270.50
Convert to an exponential equation.
180)
ln 44 = 3.7842
180)
A)
e3.7842 = ln 44
B)
e44 = 3.7842
C)
e3.7842 = 44
D)
e3.7842 = 1
Graph the function.
181)
f(x) =3x
181)
A)
B)
81
C)
D)
Find the range of the given function. Express your answer in interval notation.
182)
f(x) = – 2x2+ 12x – 23
182)
A)
[5, )
B)
(–, –3]
C)
[–3, )
D)
(–, –5]
Determine whether the function is linear, constant, or neither
183)
y =x + 3
7
183)
A)
Linear
B)
Constant
C)
Neither
Give the domain and range of the function.
184)
g(x) =x2–4
184)
A)
Domain: [4, ); Range: all real numbers
B)
Domain: all real numbers; Range: [-3, )
C)
Domain: [0, ); Range: [0, )
D)
Domain: all real numbers; Range: [–4, )
Graph the function.
82
185)
f(x) =1
2
x
185)
A)
B)
C)
D)
Find the vertex form for the quadratic function. Then find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range
186)
n(x) = – x2+ 4x – 3
186)
A)
Standard form: n(x) = – (x – 2)2+ 1
(A) x–intercepts: 1, 3; y–intercept: -3
(B) Vertex (2, 1)
(C) Maximum: 1
(D) y 1
B)
Standard form: n(x) = – (x + 2)2+ 1
(A) x–intercepts: -3, – 1; y–intercept: -3
(B) Vertex (2, 1)
(C) Maximum: 1
(D) y 1
C)
Standard form: n(x) = – (x – 2)2+ 1
(A) x–intercepts: 1, 3; y–intercept: -3
(B) Vertex (-2, -1)
(C) Maximum: 1
(D) y 1
D)
Standard form: n(x) = – (x + 2)2+ 1
(A) x–intercepts: 1, 3; y–intercept: -3
(B) Vertex (2, 1)
(C) Minimum: 1
(D) y 1
Solve the problem.
187)
Book sales on the Internet (in billions of dollars) in year x are approximated by f(x) = 1.84 + 2.1 · ln
x, where x = 0 corresponds to 2000. How much will be spent on Internet book sales in 2008? Round
to the nearest tenth.
187)
A)
8.0 billion
B)
6.2 billion
C)
3.9 billion
D)
6.0 billion
Determine the domain of the function.
188)
f(x) =x
x – 2
188)
A)
No solution
B)
x < 2
C)
All real numbers
D)
All real numbers except 2
For the given function, find each of the following:
(A) Intercepts
(B) Vertex
(C) Maximum or minimum
(D) Range
189)
f(x) =(x + 3)2– 4
189)
A)
(A) x–intercepts: – 5, -1; y–intercept: 5
(B) Vertex (-3, -4)
(C) Minimum: -4
(D) y -4
B)
(A) x–intercepts: – 5, -1; y–intercept: 5
(B) Vertex (-3, -4)
(C) Maximum: -4
(D) y -4
C)
(A) x–intercepts: – 5, -1; y–intercept: 5
(B) Vertex (3, -4)
(C) Minimum: -4
(D) y -4
D)
(A) x–intercepts: 1, 5; y–intercept: 5
(B) Vertex (-3, -4)
(C) Minimum: -4
(D) y -4
Graph by converting to exponential form first.
190)
y =log 4(x – 1)
190)
A)
B)
85
C)
D)
Solve the problem.
191)
The point at which a company’s costs equals its revenue is the break–even. C represents cost, in
dollars, of x units of a product. R represents the revenue, in dollars, for the sale of x units. Find the
number of units that must be produced and sold in order to break even.
C = 15x + 12,000
R = 18x – 6000
191)
A)
6000
B)
545
C)
800
D)
12,000
Find the equations of any vertical asymptotes.
192)
f(x) =x – 9
x2+ 6
192)
A)
x =-6
B)
x =6
C)
x =3, x =-3
D)
None
Provide an appropriate response.
193)
In a profit–loss analysis, point where revenue equals cost.
193)
A)
inflection point
B)
turning point
C)
break–even point
D)
profit–loss point
Answer Key
Testname: C2
87
Answer Key
Testname: C2
Answer Key
Testname: C2
Answer Key
Testname: C2
Answer Key
Testname: C2