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.
79)
f(x) =x2– 2x – 8, g(x) = x – 4
79)
A)
x + 2; x 4
B)
x + 2; x –4
C)
x + 4; x 2
D)
x + 2; x 0
Decide whether the relation is a function.
80)
80)
A)
Function
B)
Not a function
Determine whether the variation between the indicated quantities is direct or inverse.
81)
The distance traveled by you in a car and the time taken to drive this distance
81)
A)
Inverse
B)
Direct
Find (f
g)(x) for the given functions f(x) and g(x).
82)
f(x) =7x + 5 and g(x) = x2– 2
82)
A)
7x2– 9
B)
x2+ 7x + 3
C)
x2– 7x – 7
D)
49x2+ 14x – 5
Decide whether the relation is a function.
83)
x–9–9 1 4 9
y 2 1 5 5 –8
83)
A)
Function
B)
Not a function
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.
84)
f(x) = 27x3– 216, g(x) = 3x – 6
84)
A)
9x2+ 18x + 36; x 2
B)
3x2+ 6x + 36; x –2
C)
10x2+ 20x + 35; x 2
D)
9x2– 18x + 36; x 0
Evaluate the composition of functions.
85)
Let f(x) =5x +4 and g(x) = x +8. Find (f
g)(2).
85)
A)
24
B)
140
C)
22
D)
54
Decide whether the relation is a function.
86)
{(–9, 3), (–9, 5), (–1, 3), (5, –9), (10, –9)}
86)
A)
Function
B)
Not a function
Solve the problem.
87)
Find f(k) when f(x) = 3x2+ 4x + 5.
87)
A)
3k2+ 4k + 5
B)
3k2+ 16k + 5
C)
3k2+ 4k + 25
D)
9k2+ 16k + 25
22
Graph the linear function. Give the domain and range.
88)
f(x) =2x + 4
88)
A)
Domain: (–, )
Range: (–, )
B)
Domain: (–, )
Range: (–, )
Find (f
g)(x) for the given functions f(x) and g(x).
89)
f(x) =5x + 13 and g(x) =2x – 1
89)
A)
10x + 18
B)
10x + 8
C)
10x + 25
D)
10x + 12
For the given pair of functions, find the requested function.
90)
f(x) =4x –3, g(x) = – 7x +10; (f + g)(x)
90)
A)
–3x +7
B)
–3x2+7
C)
–4x +13
D)
11x – 7
23
Evaluate the function.
91)
Find f(12)
f
91)
A)
4
B)
7
C)
None of these
D)
(7, 4)
Solve the problem.
92)
If f varies jointly as q2 and h, and f =96 when q =4 and h =3, find q when f =40 and h =5.
92)
A)
2
B)
4
C)
3
D)
5
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.
93)
f(x) =x2+11x +24, g(x) = x +8
93)
A)
x +11; x
0
B)
x +3; x 8
C)
x +3; x –8
D)
x +8; x –3
For the given pair of functions, find the requested function.
94)
f(x) =x2+6x +6 and g(x) =5x –2; (fg)(1)
94)
A)
–17
B)
39
C)
13
D)
37
24
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.
95)
f(x) = 7x2– 44x – 35, g(x) = x – 7
95)
A)
7x – 5; x –7
B)
7x + 5; x –7
C)
7x + 5; x
7
D)
7x – 5; x
7
Solve the problem.
96)
If m varies directly as p, and m =18 when p =6, find m when p is 4.
96)
A)
12
B)
36
C)
9
D)
16
For the pair of functions, find the product (fg)(x).
97)
f(x) =5x, g(x) =7x –6
97)
A)
35x2–30x
B)
–35x2–30x
C)
35x –30
D)
12x2–6x
For the given pair of functions, find the requested function.
98)
f(x) =x2– x –8 and g(x) = x – 1; (fg)(x)
98)
A)
x3– 2x2–8x +8
B)
x3– 2x2–7x +8
C)
x3–7x +8
D)
x3– 2x2–9x –8
Solve the problem.
99)
The resistance of a wire varies directly as the length of the wire and inversely as the square of the
diameter of the wire. A 20 foot length of wire with a diameter of 0.1 inch has a resistance of 3 ohms.
What would the resistance be for a 40 foot length, with diameter 0.01 inch, of the same kind of wire
?
99)
A)
18 ohms
B)
–1 ohms
C)
3.5 ohms
D)
6 ohms
100)
The mathematical model f(x) =700x + 100,000 represents the cost in dollars a company has in
producing x items during a month. Based on this, how much does it cost to produce 200 items?
Interpret the question and answer using function notation.
100)
A)
$140,000; f(200) =140,000
B)
$240,000; f(240,000) =200
C)
$140,000; f(140,000) =200
D)
$240,000; f(200) =240,000
101)
The table represents a linear function. Find the slope and y–intercept of the line and use your
answers to write an equation for f(x).
x y = f(x)
04.8
13.3
21.8
30.3
4–1.2
5–2.7
101)
A)
f(x) = – 1.5x +4.8
B)
f(x) =4.8x –1.5
C)
f(x) = – 4.8x +1.5
D)
f(x) =1.5x +4.8
Decide whether the relation is a function, and give the domain and range.
102)
102)
A)
Not a function; domain: (–, –3]; range: (–, )
B)
Function; domain: (–, ); range: (–, –3]
C)
Function; domain: (–, –3]; range: (–, )
D)
Not a function; domain: (–, ); range: (–, –3]
Solve the problem.
103)
Find f(0) when f(x) = x2+ 3x + 7.
103)
A)
10
B)
49
C)
–7
D)
7
Evaluate the function.
104)
Find f(3).
x y = f(x)
327
1 3
0 0
–1 3
–327
104)
A)
1
B)
27
C)
3
D)
0
Graph the linear function. Give the domain and range.
105)
g(x) = x – 4
105)
A)
Domain: (–, )
Range: (–, )
B)
Domain: (–, )
Range: (–, )
Decide whether the relation is a function.
106)
{(–1, –3), (3, 9), (5, –5), (7, 8), (12, –3)}
106)
A)
Not a function
B)
Function
Decide whether the relation is a function, and give the domain and range.
107)
107)
A)
Not a function; domain: [–5, 1]; range: [–3, 1]
B)
Function; domain: [–3, 1]; range: [–5, 1]
C)
Function; domain: [–5, 1]; range: [–3, 1]
D)
Not a function; domain: [–3, 1]; range: [–5, 1]
Determine whether the variation between the indicated quantities is direct or inverse.
108)
The weight of a baby in pounds and his age in months
108)
A)
Direct
B)
Inverse
For the polynomial function, find the requested value.
109)
f(x) =2x + 9; f(4)
109)
A)
16
B)
–1
C)
17
D)
11
110)
f(x) = – 2x5+ 5x4– 5x3–x2; f(2)
110)
A)
1
B)
–32
C)
–33
D)
–28
29
Solve the problem.
111)
Find f(–4) when f(x) = – x2+ 2x – 1.
111)
A)
7
B)
9
C)
– 25
D)
23
Decide whether the relation is a function.
112)
112)
A)
Function
B)
Not a function
113)
{(–5, 1), (–1, –4), (–1, –1), (–1, 7)}
113)
A)
Function
B)
Not a function
Determine whether the equation represents direct, inverse, joint, or combined variation.
114)
y =6x2z3
114)
A)
Direct
B)
Inverse
C)
Joint
D)
Combined
Determine whether the relation defines y as a function of x. Give the domain.
115)
y = x3
115)
A)
Not a function; domain: (–,)
B)
Not a function; domain: all whole numbers
C)
Function; domain: (–,)
D)
Function; domain: all whole numbers
Find the requested value.
116)
If p(x) =12x3+ 38x2– 38x – 1 and q(x) =2x +8, find ( p
q)(4).
116)
A)
0
B)
1529
16
C)
1223
24
D)
1223
16
Solve the problem.
117)
If f varies jointly as q2 and h, and f =108 when q =3 and h =4, find h when f =525 and q =5.
117)
A)
4
B)
3
C)
5
D)
7
Decide whether the relation is a function.
118)
{(–6, 5), (–4, 9), (–2, –4), (2, 6)}
118)
A)
Not a function
B)
Function
Solve the problem.
119)
A truck rental company charges $35, plus $0.09 per mile to rent a moving truck for a day. If x
represents the number of miles driven and f(x) represents the total cost to rent the truck for a day,
write a linear function that models the situation.
119)
A)
f(x) =0.09x –35
B)
f(x) =35x +0.09
C)
f(x) =0.09x +35
D)
f(x) =0.09x +35x
120)
For a fixed amount of principal, the simple interest varies jointly with the rate and the time. If the
simple interest is $1200 when the rate is 4% and the time is 6 years, find the simple interest when
the rate is 5% and the time is 10 years.
120)
A)
$2500
B)
$250
C)
$2750
D)
$5000
Provide an appropriate response.
121)
Let f(x) =x2–1 and g(x) =2x +8. Find (f – g)(2).
121)
A)
–8
B)
–9
C)
–11
D)
–4
Solve.
122)
The speed of a vehicle varies inversely as the time it takes to travel a fixed distance. If a vehicle
travels a fixed distance at 45 miles per hour in 20 minutes, how fast must it travel to cover the same
distance in 10 minutes?
122)
A)
40
9 mph
B)
2
45 mph
C)
45
2 mph
D)
90 mph
Evaluate the function.
123)
The graph of y = f(x) is shown below. Find f(4)
123)
A)
–5
B)
–1
C)
4
D)
1
Determine whether the variation between the indicated quantities is direct or inverse.
124)
The price of an item and the quantity of the item that you can purchase with a given amount of
money
124)
A)
Direct
B)
Inverse
32
Solve the problem.
125)
A truck rental company charges $25 plus $0.13 per mile to rent a moving truck for a day. If x
represents the number of miles driven and f(x) represents the total cost to rent the truck for a day, a
linear function that models the situation is f(x) =0.13x +25. What is the cost of renting the truck if it
is driven 200 miles?
125)
A)
$1.00
B)
$5000.13
C)
$51.00
D)
$27.60
Determine whether the relation defines y as a function of x. Give the domain.
126)
x =y4
126)
A)
Function; domain: (–,)
B)
Function; domain: [0, )
C)
Not a function; domain: [0, )
D)
Not a function; domain: (–,)
Decide whether the relation is a function, and give the domain and range.
127)
127)
A)
Function; domain: {–3, 3}; range: {–3, 0, 6}
B)
Function; domain: {–3, 0, 6}; range: {–3, 3}
C)
Not a function; domain: {–3, 3}; range: {–3, 0, 6}
D)
Not a function; domain: {–3, 0, 6}; range: {–3, 3}
Decide whether the relation is a function.
128)
x–3 2 6 7 12
y 8 7 –5 8 8
128)
A)
Function
B)
Not a function
129)
{(–8, 2), (–8, 8), (1, 5), (6, 2), (8, 9)}
129)
A)
Function
B)
Not a function
Solve the problem.
130)
Find g(a + 1) when g(x) =5x + 2.
130)
A)
5a – 1
B)
5a + 2
C)
5a + 7
D)
1
5a + 2
131)
Suppose the sales of a particular brand of appliance are modeled by the linear function
S(x) =250x + 4000, where S(x) represents the number of sales in year x, with x = 0 corresponding to
1982. Find the number of sales in 1990.
131)
A)
11,750 sales
B)
6000 sales
C)
5750 sales
D)
12,000 sales
Answer the question.
132)
The function f(x) = 60x computes the number of minutes in x hours. The function g(x) = 24x
computes the number of hours in x days. What is (f
g)(x) and what does it compute?
132)
A)
(f
g)(x) = 84x; it computes the number of minutes plus the number of days in x days.
B)
(f
g)(x) = 1440x; it computes the number of minutes in x days.
C)
(f
g)(x) = 1440x; it computes the number of days in x minutes.
D)
(f
g)(x) = 1440x2; it computes the number of minutes in x days.
For the polynomial function, find the requested value.
133)
f(x) =4x3– 6x2– x + 11; f(–2)
133)
A)
–7
B)
–43
C)
–53
D)
–55
For the given pair of functions, find the requested function.
134)
f(x) = x2– 2 and g(x) =5x + 8; (g
f)(x)
134)
A)
x2+ 5x + 6
B)
25x2+ 10x – 8
C)
x2– 5x – 10
D)
5x2– 2
Decide whether the relation is a function, and give the domain and range.
135)
135)
A)
Not a function; domain: [3, ); range: ( , )
B)
Function; domain: [3, ); range: ( , )
C)
Function; domain: (–, ); range: [3, )
D)
Not a function; domain: (–, ); range: [3, )
Solve the problem.
136)
Rental on a car is $130 plus $0.02 per mile. If x represents the number of miles driven and f(x)
represents the total cost to rent the car, a linear function that models the situation is
f(x) =0.02x +130. Find the value of x if f(x) =178. Interpret your answer in the context of this
problem.
136)
A)
2400; It costs $2400 to drive the rental car 178 miles.
B)
134; It costs $134 to drive the rental car 178 miles.
C)
2400; It costs $178 to drive the rental car 2400 miles.
D)
134; It costs $178 to drive the rental car 134 miles.
Determine whether the variation between the indicated quantities is direct or inverse.
137)
The balance on your credit card and the amount of available credit
137)
A)
Direct
B)
Inverse
Determine whether the relation defines y as a function of x. Give the domain.
138)
3x =8– 5y
138)
A)
Function; domain: all integers
B)
Function; domain: (–,)
C)
Not a function; domain: (–,)
D)
Not a function; domain: all whole numbers
Solve the problem.
139)
If the height of a rectangular solid is held constant, the volume varies jointly with the length and
the width. If the volume is 180 cubic inches when the length is 9 inches and the width is 5 inches,
find the volume when the length is 8 inches and the width is 6 inches.
139)
A)
192 in.3
B)
144 in.3
C)
160 in.3
D)
216 in.3