A)
B)
C)
D)
D)
Solve the problem.
118)
The total cost in dollars for a certain company to produce x empty jars to be used by a jelly
producer is given by the function C(x) =0.8x +40,000. Find C(50,000), the cost of producing 50,000
jars.
118)
A)
B)
C)
$40.80
D)
D)
Determine whether the equation defines y as a function of x.
119)
y2=5x
119)
A)
y is a function of x
B)
y is not a function of x
Evaluate the function at the given value of the independent variable and simplify.
120)
f(x) = – 5x + 1;f(–3)
120)
A)
B)
C)
16
D)
Find the distance between the pair of points.
121)
(–1, 3) and (–4, –1)
121)
A)
B)
C)
25
D)
D
Determine whether the relation is a function.
122)
{(–8, –9), (–8, 9), (1, 3), (3, 5), (10, –9)}
122)
A)
Function
B)
Not a function
B
C
Use the graph of f to draw the graph of its inverse function.
123)
123)
A)
B)
Find the domain of the function.
124)
f(x) = x –7
x + 8
124)
A)
(–, –8)
(–8, )
B)
(–, )
C)
(–, 7)
(7, )
D)
(–, –8)
(–8, 7)
(7, )
A
63
A
Find and simplify the difference quotient f(x +
h) – f(x)
h, h
0 for the given function.
125)
f(x) =1
5x
125)
A)
B)
C)
–1
5x (x + h)
D)
Find the average rate of change of the function from x1 to x2.
126)
f(x) = 5x + 7 from x1= – 1 to x2= 0
126)
A)
B)
C)
5
D)
C
Determine whether the given function is even, odd, or neither.
127)
f(x) = x3– x2
127)
A)
Neither
B)
Odd
C)
Even
A
Find the distance between the pair of points.
128)
(7, 3) and (–2, –7)
128)
A)
B)
C)
181
D)
C
Graph the equation.
64
C
129)
2x –5y + 16 = 0
129)
A)
B)
C)
D)
65
Solve the problem.
130)
Along with incomes, people’s charitable contributions have steadily increased over the past few
years. The table below shows the average deduction for charitable contributions reported on
individual income tax returns for the period 1993 to 1998. Find the average annual increase
between 1995 and 1997.
Year Charitable Contributions
1993 $1950
1994 $2440
1995 $2480
1996 $2770
1997 $3030
1998 $3160
130)
A)
B)
C)
$550 per year
D)
Find the average rate of change of the function from x1 to x2.
131)
f(x) =2x from x1= 2 to x2= 8
131)
A)
B)
C)
–3
10
D)
Find an equation for the line with the given properties.
132)
The solid line L contains the point (3, 4) and is perpendicular to the dotted line whose equation is
y =2x. Give the equation of line L in slope–intercept form.
132)
A)
y – 4 = – 1
2(x – 3)
B)
y =1
2x +11
2
C)
y = – 1
2x +11
2
D)
y – 4 = 2(x – 3)
The graph of a function f is given. Use the graph to answer the question.
133)
Find the numbers, if any, at which f has a relative maximum. What are the relative maxima?
133)
A)
f has a relative maximum at x =3; the relative maximum is 1
B)
f has a relative maximum at x = – 3 and 3; the relative maximum is 0
C)
f has a relative maximum at x = 0; the relative maximum is 1
D)
f has no relative maximum
Use the graph to determine the function’s domain and range.
134)
134)
A)
domain: (–, 3) or (3, )
range: (–, 3) or (3, )
B)
domain: (–, )
range: (–, 3]
C)
domain: (–, )
range: (–, )
D)
domain: (–, 3]
range: (–, 3]
Use the given conditions to write an equation for the line in the indicated form.
135)
Passing through (2, –3) and parallel to the line whose equation is y = – 8x +2;
slope–intercept form
135)
A)
B)
C)
y = – 8x + 13
D)
C
Given functions f and g, determine the domain of f +
g.
136)
f(x) =3x2– 1, g(x) =2x3+ 8
136)
A)
(–, –3) or (–3, –2) or (–2, )
B)
(0, )
C)
(–, )
D)
(–, 0) or (0, )
C
68
B
Use the given conditions to write an equation for the line in the indicated form.
137)
Passing through (5, 4) and parallel to the line whose equation is y = – 1
6x +2;
slope–intercept form
137)
A)
B)
C)
y = – 6x – 29
D)
138)
Passing through (2, 5) and perpendicular to the line whose equation is –8x + y –8= 0;
slope–intercept form
138)
A)
B)
C)
y = – 8x – 42
D)
Give the domain and range of the relation.
139)
{(–6, –3), (–8, –1), (–4, –7), (8, 2), (5, –4)}
139)
A)
domain = {8, –4, –6, –8, 5}; range = {2, –7, –3, –1, –4}
B)
domain = {2, –7, –3, –1, –4}; range = {8, –4, –6, –8, 5}
C)
domain = {–3, –8, –1, 5, –4}; range = {8, 2, –4, –7, –6}
D)
domain = {8, 2, –4, –7, –6}; range = {–3, –8, –1, 5, –4}
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
140)
f(x) =x, g(x) =x+2
140)
69
A)
g shifts the graph of f vertically down 2units
B)
g shifts the graph of f vertically up 2units
C)
g shifts the graph of f vertically down 2units
70
D)
g shifts the graph of f vertically up 2units
Identify the intervals where the function is changing as requested.
141)
Increasing
141)
A)
B)
C)
(–2, 2)
D)
C
D)
Write the standard form of the equation of the circle with the given center and radius.
142)
(10, 0); 1
142)
A)
(x – 10)2+ y2=1
B)
x2+ (y – 10)2=1
C)
x2+ (y + 10)2=1
D)
(x + 10)2+ y2=1
A
D
D)
Graph the linear function by plotting the x– and y–intercepts.
143)
0.3x + 0.4y –2.4 = 0
143)
A)
intercepts: (0, –6), (8, 0)
B)
intercepts: (0, –6), (–8, 0)
C)
intercepts: (0, 6), (–8, 0)
D)
intercepts: (0, 6), (8, 0)
72
For the given functions f and g , find the indicated composition.
144)
f(x) = x2– 2x – 5,g(x) = x2+ 2x + 2
(f
g)(–4)
144)
A)
B)
C)
336
D)
Determine which two functions are inverses of each other.
145)
f(x) =3x g(x) =x
3h(x) =3
x
145)
A)
B)
C)
None
D)
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
146)
f(x) =2x2, g(x) =2x2–3
146)
A)
g shifts the graph of f vertically up 3units
73
B)
g shifts the graph of f vertically down 3units
C)
g shifts the graph of f vertically up 3units
D)
g shifts the graph of f vertically down 3units
Find the domain of the function.
147)
f(x) =1
x – 5
147)
A)
B)
C)
(–, 0)
(0, )
D)
Determine the slope and the y–intercept of the graph of the equation.
148)
10x + y + 9 = 0
148)
A)
m = – 10
9; 0, –1
9
B)
m = – 1
10 ; 0, –9
10
C)
m =10; (0, –9)
D)
m = – 10; (0, –9)
D
Given functions f and g, determine the domain of f +
g.
149)
f(x) =2x – 2,g(x) =2
x +7
149)
A)
(–, –2) or (–2, )
B)
(0, )
C)
(–, –7) or (–7, )
D)
(–, )
C
Find and simplify the difference quotient f(x +
h) – f(x)
h, h
0 for the given function.
150)
f(x) =3x2
150)
A)
3(2x+h)
B)
3
C)
6
h+ x +3h
D)
3(2x2+ 2xh +h2)
h
A
A
Identify the intervals where the function is changing as requested.
151)
Decreasing
151)
A)
B)
C)
(–, –2)
D)
Write the standard form of the equation of the circle with the given center and radius.
152)
(0, 0); 14
152)
A)
B)
C)
x2+y2=196
D)
Determine the slope and the y–intercept of the graph of the equation.
153)
y – 11 = 0
153)
A)
m = 1; (0, 11)
B)
m =11; (0, 0)
C)
m = 0; (0, 11)
D)
m = 0; no y–intercept
Graph the equation.
76
154)
3x – 5y + 11 = 0
154)
A)
B)
C)
D)
Answer:
A
Explanation:
A)
B)
C)
D)
77
Solve.
155)
A vendor has learned that, by pricing caramel apples at $1.50, sales will reach 82 caramel apples
per day. Raising the price to $2.50 will cause the sales to fall to 34 caramel apples per day. Let y be
the number of caramel apples the vendor sells at x dollars each. Write a linear equation that
models the number of caramel apples sold per day when the price is x dollars each.
155)
A)
y = – 1
48 x +2623
32
B)
y =48x + 10
C)
y = – 48x +154
D)
y = – 48x –154
Solve the problem.
156)
A deep sea diving bell is being lowered at a constant rate. After 11 minutes, the bell is at a depth of
300 ft. After 30 minutes the bell is at a depth of 1900 ft. What is the average rate of lowering per
minute? Round to the nearest hundredth is needed.
156)
A)
84.2 ft per minute
B)
53.3 ft per minute
C)
63.3 ft per minute
D)
0.01 ft per minute
Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
157)
157)
A)
function
B)
not a function
Given functions f and g, perform the indicated operations.
158)
f(x) =3x – 4,g(x) =9x – 6
Find f – g.
158)
A)
B)
C)
6x – 2
D)
Evaluate the function at the given value of the independent variable and simplify.
159)
g(x) =3x + 1;g(x + 1)
159)
A)
B)
C)
3x + 1
D)
A
Use the given conditions to write an equation for the line in the indicated form.
160)
Passing through (4, 5) and perpendicular to the line whose equation is y =4x + 7;
point–slope form
160)
A)
y –5= – 1
4(x –4)
B)
y = – 4x – 24
C)
y –4=1
4(x –5)
D)
y –5=1
4(x +4)
A
79
A
The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the
graph to answer the question.
161)
If f(x) =15%, what year is represented by x?
161)
A)
B)
C)
1985
D)
Evaluate the piecewise function at the given value of the independent variable.
162)
h(x) =
x2– 7
x + 6 if x –6
x – 2 if x = – 6
; h(–6)
162)
A)
B)
C)
–4
D)
Find the domain of the function.
163)
f(x) =5x + 3
163)
A)
B)
C)
(–, 0)
(0, )
D)
80