140)
The current I in an electrical conductor varies inversely as the resistance R of the conductor. The
current is 4 amperes when the resistance is 842 ohms. What is the current when the resistance is 803
ohms?
140)
A)
3.8 amps
B)
0.26 amps
C)
4.2 amps
D)
0.24 amps
Determine whether the variation between the indicated quantities is direct or inverse.
141)
The time it takes to drive 100 miles and the speed at which you drive
141)
A)
Direct
B)
Inverse
Solve the problem.
142)
The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical
container 3 cm on a side is 54 g, find the weight of the liquid in a cubical container 4 cm on a side.
142)
A)
8 g
B)
128 g
C)
52 g
D)
64 g
143)
The function H described by H(x) = 2.75x + 71.48 can be used to estimate the height, in centimeters,
of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the
height of a woman whose humerus is 31.4 cm long.
143)
A)
105.63 cm
B)
42.83 cm
C)
14.87 cm
D)
157.83 cm
Determine whether the relation defines y as a function of x. Give the domain.
144)
y = – 9
x
144)
A)
Function; domain: (–,)
B)
Not a function; domain (–, 9) (9, )
C)
Not a function; domain (–, 0)(0, )
D)
Function; domain (–, 0)(0, )
Solve the problem.
145)
The volume of a gas varies inversely as the pressure and directly as the temperature (in Kelvin). If a
certain gas occupies a volume of 2.3 liters at a temperature of 380 K and a pressure of 20 newtons
per square centimeter, find the volume when the temperature is 494 K and the pressure is
10 newtons per square centimeter. Round your answer to the nearest tenth.
145)
A)
6.0 L
B)
0.9 L
C)
35.4 L
D)
43.7 L
Decide whether the relation is a function.
146)
146)
A)
Function
B)
Not a function
Solve the problem.
147)
If s varies directly as t2, and s =175 when t =5, find s when t is 3.
147)
A)
35
B)
63
C)
15
D)
105
For the polynomial function, find the requested value.
148)
f(x) = – 6x3+ 4x2+ 2; f(2)
148)
A)
–30
B)
–38
C)
–40
D)
–42
Solve the problem.
149)
If x varies inversely as y2, and x =3 when y =20, find x when y =5.
149)
A)
75
B)
36
C)
48
D)
4
Decide whether the relation is a function.
150)
{(–4, 1), (–3, –6), (3, –8), (3, 4)}
150)
A)
Not a function
B)
Function
Find the requested value.
151)
If f(x) =x2+4x +3 and g(x) =6x –1, find (fg)(–3).
151)
A)
–414
B)
32
C)
0
D)
18
For the given pair of functions, find the requested function.
152)
f(x) =5x –4 and g(x) = – 9x2–14x +9; (f + g)(x)
152)
A)
–10x2–9x –5
B)
–9x2–9x +5
C)
–9x2+9x +5
D)
9x2– 4x –13
Determine whether the relation defines y as a function of x. Give the domain.
153)
xy =9
153)
A)
Function; domain: (–, 0)(0, )
B)
Not a function; domain: (–, 0)(0, )
C)
Not a function; domain: ( , )
D)
Function; domain: ( , )
Solve the problem.
154)
Crafty Bill’s Cool Car Sales opened as a used car sales lot in 1991. The graph shows the number of
cars sold as a function of time. Is this the graph of a function? What is the domain?
154)
A)
Function; Domain: [2005, 2011]
B)
Not a function; Domain: [2007, 2011]
C)
Function; Domain: [2007, 2011]
D)
Not a function; Domain: [2005, 2011]
Determine whether the equation represents direct, inverse, joint, or combined variation.
155)
y =6
x
155)
A)
Combined
B)
Inverse
C)
Direct
D)
Joint
For the given pair of functions, find the requested function.
156)
f(x) =x2+5x –3, g(x) = – 8x2+7x –6; (f – g)(x)
156)
A)
–8x2–12x +3
B)
–7x2+12x –3
C)
9x2–9x +9
D)
9x2–2x +3
40
An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation
f(x).
157)
5x – 6y = 5
157)
A)
f(x) = 5 –5x
6
B)
f(x) =5 – 5x
–6
C)
f(x) = – 5x –5
6
D)
f(x) = 5 – 5x
For the polynomial function, find the requested value.
158)
f(x) =4x2– 3x – 8; f(3)
158)
A)
–5
B)
15
C)
19
D)
9
159)
f(x) = – 8x + 5; f(2)
159)
A)
–21
B)
–3
C)
–11
D)
–32
For the given pair of functions, find the requested function.
160)
f(x) =24x3– 20x2– 8x – 54 and g(x) =6x +7; f
g(1)
160)
A)
50
13
B)
–58
13
C)
0
D)
–6
7
Determine whether the relation defines y as a function of x. Give the domain.
161)
x =y2– 7
161)
A)
Function; domain: ( , )
B)
Function; domain: (–7, )
C)
Not a function; domain: ( , )
D)
Not a function; domain: (–7, )
Solve the problem.
162)
The volume V of a given mass of gas varies directly as the temperature T and inversely as the
pressure P. If V =88.0 in.3 when T =110° and P =15 lb/in.2, what is the volume when T =230° and
P =15 lb/in.2?
162)
A)
184.0 in.3
B)
174.0 in.3
C)
144.0 in.3
D)
224.0 in.3
For the pair of functions, find the product (fg)(x).
163)
f(x) =5x +4, g(x) = – x2+4x +7
163)
A)
–5x3–17x2+51x –28
B)
5x3+16x2–51x –28
C)
–10x2+16x2–51x +28
D)
–5x3+16x2+51x +28
Give the domain and range of the relation shown in the following.
164)
164)
A)
Domain: (–, 3]; range: (–, )
B)
Domain: (3, ); range: (–, )
C)
Domain: [3, ); range: (–, )
D)
Domain: (–, ); range: (–, 3]
42
Find (f
g)(x) for the given functions f(x) and g(x).
165)
f(x) =3x + 7 and g(x) =3x – 7
165)
A)
9x – 14
B)
14
C)
6x
D)
9x + 14
An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation
f(x).
166)
9x2+ 7y = 6
166)
A)
f(x) =6 + 9x2
7
B)
f(x) = – 9x2+6
7
C)
f(x) = 6 – 9x2
D)
f(x) =6 – 9x2
7
For the polynomial function, find the requested value.
167)
f(x) =5x3+ 6x2– 16; f(–2)
167)
A)
–42
B)
–44
C)
–68
D)
–32
For the pair of functions, find the quotient f
g(x) and give any x–values that are not in the domain of the quotient
function.
168)
f(x) =45x2–5x, g(x) =5x
168)
A)
9x – 1; x 5
B)
9x2; x 5
C)
225x3–25x2; x 0
D)
9x – 1; x 0
Solve the problem.
169)
The volume of wood in a tree varies jointly as the height of the tree and the square of the distance
around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the
distance around the trunk is 3 feet, what is the volume of wood obtained from a tree that is 32 feet
tall having a measurement of 4 feet around the trunk?
169)
A)
44.96 ft3
B)
32.96 ft3
C)
49.96 ft3
D)
40.96 ft3
Evaluate the function.
170)
The graph of y = f(x) is shown below. Find f(–1)
170)
A)
7
B)
3
C)
–3
D)
5
Find the requested value.
171)
If f(x) =x2+5x +1 and g(x) =4x –2, find (fg)(x).
171)
A)
16x2+ 4x – 5
B)
4x3+ 18x2+5x –2
C)
4x3– 18x2+ 6x – 2
D)
4x3+ 18x2– 6x – 2
44
Solve the problem.
172)
It has been determined that the number of fish f(t) that can be caught in t minutes in a certain pond
using a certain bait is f(t) = 0.25t + 1, for t > 10. Find the number of fish that can be caught if you
fish for 14 minutes. Round your answer to the nearest whole number.
172)
A)
18 fish
B)
16 fish
C)
5 fish
D)
10 fish
173)
Find f(a) when f(x) = – x2+ 3x – 1.
173)
A)
–a2+ 3a – 1
B)
–3a
C)
–a2+ 3a
D)
a2+ 3a – 1
For the given pair of functions, find the requested function.
174)
f(x) =x2+4 and g(x) =2x +6; (g
f)(7)
174)
A)
100
B)
112
C)
404
D)
59
Determine whether the equation represents direct, inverse, joint, or combined variation.
175)
y =5x
st
175)
A)
Combined
B)
Direct
C)
Inverse
D)
Joint
Decide whether the relation is a function, and give the domain and range.
176)
176)
A)
Function; domain: (–, 0)
(0, ); range: (–, )
B)
Not a function; domain: (–, ); range: (–, )
C)
Function; domain: (–, ); range: (–, )
D)
Not a function; domain: (–, 0)
(0, ); range: (–, )
177)
177)
A)
Not a function; domain: (–, –3] ; range: (–, )
B)
Function; domain: (–, ) ; range: (–, )
C)
Function; domain: (–, –3] ; range: (–, )
D)
Not a function; domain: (–, ) ; range: (–, )
For the given pair of functions, find the requested function.
178)
f(x) =4x –2, g(x) = – 7x2–9x +6; (f – g)(x)
178)
A)
7x2–5x –8
B)
–7x2–5x +4
C)
7x2+13x –8
D)
–7x2+13x +8
Determine whether the variation between the indicated quantities is direct or inverse.
179)
The number of hours worked by an hourly worker and the amount of her paycheck
179)
A)
Direct
B)
Inverse
For the given pair of functions, find the requested function.
180)
f(x) =x2+4x –4, g(x) = – 7x2+10x –3; (f + g)(x)
180)
A)
–8x2+14x +7
B)
–6x2+14x –7
C)
–6x2–14x –7
D)
–7x2+14x +7
Provide an appropriate response.
181)
Let f(x) =x2–2 and g(x) =4x +7. Find (f + g)( 1
3).
181)
A)
58
9
B)
59
9
C)
19
3
D)
62
9
Answer Key
Testname: C9
Answer Key
Testname: C9
Answer Key
Testname: C9
Answer Key
Testname: C9