122)
–1
2x + y –4= 0
122)
A)
intercepts: (0, 4), (–8, 0)
B)
intercepts: (0, 4), (–4, 0)
C)
intercepts: (0, 4), (8, 0)
D)
intercepts: (0, –8), (8, 0)
Find the inverse of the one–to–one function.
123)
f(x) =7
3x – 1
123)
A)
f–1(x) = – 1
3–7
3x
B)
f–1(x) =7
3y +1
3
C)
f–1(x) =7
3x +1
3
D)
f–1(x) =3x – 1
7
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
124)
f(x) = x, g(x) = x –2
124)
A)
g shifts the graph of f vertically down 2units
62
B)
g shifts the graph of f vertically up 2units
C)
g shifts the graph of f vertically down 2units
D)
g shifts the graph of f vertically up 2units
Use the given conditions to write an equation for the line in the indicated form.
125)
Passing through (2, –3) and parallel to the line whose equation is y = – 8x +2;
slope–intercept form
125)
A)
y =8x – 13
B)
y = – 8x – 13
C)
y = – 1
8x –13
8
D)
y = – 8x + 13
Identify the intercepts.
126)
126)
A)
(–1, –1), (1, 1)
B)
(–1, 0), (0, 1)
C)
(1, 0), (0, 1)
D)
(–1, 0), (0, –1)
Find the center and the radius of the circle.
127)
(x + 2)2+ (y – 6)2=81
127)
A)
(2, –6), r =81
B)
(–6, 2), r =81
C)
(6, –2), r =9
D)
(–2, 6), r =9
64
Solve the problem.
128)
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
128)
A)
$550 per year
B)
$340 per year
C)
$295 per year
D)
$275 per year
Graph the equation.
129)
x2+ y2– 10x – 12y + 52 = 0
129)
A)
B)
65
Identify the intervals where the function is changing as requested.
130)
Increasing
130)
A)
(–2, 0)
B)
(–2, )
C)
(3, )
D)
(3, 6)
Evaluate the piecewise function at the given value of the independent variable.
131)
f(x) =x – 1 if x > – 3
–(x – 1) if x –3; f(–5)
131)
A)
–6
B)
–5
C)
17
D)
6
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
132)
f(x) = – 2x, g(x) = – 2x –3
132)
66
A)
g shifts the graph of f vertically down 3units
B)
g shifts the graph of f vertically up 3units
C)
g shifts the graph of f vertically up 3units
67
D)
g shifts the graph of f vertically down 3units
Find the inverse of the one–to–one function.
133)
f(x) =8x + 5
3
133)
A)
f–1(x) =3x – 5
8
B)
f–1(x) =3
8x – 5
C)
f–1(x) =3x + 5
8
D)
f–1(x) =3
8x + 5
68
Graph the equation.
134)
x2+ y2+ 6x + 4y – 12 = 0
134)
A)
B)
Determine which two functions are inverses of each other.
135)
f(x) =3x g(x) =x
3h(x) =3
x
135)
A)
f(x) and g(x)
B)
None
C)
f(x) and h(x)
D)
g(x) and h(x)
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
69
136)
f(x) =x, g(x) =x +3
136)
A)
g shifts the graph of f 3units to the left
B)
g shifts the graph of f vertically up 3units
70
C)
g shifts the graph of f 3units to the right
D)
g shifts the graph of f vertically down 3units
Find the slope of the line that goes through the given points.
137)
(–1, 1) and ( 1
2, 4)
137)
A)
1
2
B)
10
3
C)
2
D)
–1
2
Write the standard form of the equation of the circle with the given center and radius.
138)
(0, 10); 4
138)
A)
(x + 10)2+ y2=16
B)
x2+ (y + 10)2=4
C)
x2+ (y – 10)2=16
D)
(x – 10)2+ y2=16
Use the given conditions to write an equation for the line in slope–intercept form.
139)
Slope =4
7, y–intercept =2
139)
A)
f(x) = – 4
7x – 2
B)
f(x) =4
7x – 2
C)
f(x) =7
4x +7
2
D)
f(x) =4
7x + 2
Give the domain and range of the relation.
140)
{(5, –4), (1, –3), (1, 0), (10, 3), (26, 5)}
140)
A)
domain: {–4, –3, 3, 5}; range: {5, 10, 1, 26}
B)
domain: {–4, –3, 0, 3, 5}; range: {5, 10, 1, 26}
C)
domain: {5, 10, 1, 26}; range: {–4, –3, 0, 3, 5}
D)
domain: {5, 10, 1, 26}; range: {–4, –3, 3, 5}
Find the domain of the function.
141)
f(x) =1
x – 5
141)
A)
(–, )
B)
(5, )
C)
(–, 0)
(0, )
D)
(–, 5)
(5, )
Begin by graphing the standard cube root function f(x) =3x Then use transformations of this graph to graph the given
function.
72
142)
g(x) =3x+ 3
142)
A)
B)
C)
D)
Find the domain of the composite function f
g.
143)
f(x) =3x +12;g(x) =x
143)
A)
[–4, )
B)
(–, )
C)
(–, –4] or [0, )
D)
[0, )
D
73
C
Does the graph represent a function that has an inverse function?
144)
144)
A)
No
B)
Yes
For the given functions f and g , find the indicated composition.
145)
f(x) =x – 10
4,g(x) =4x + 10
(g
f)(x)
145)
A)
4x + 30
B)
x –5
2
C)
x
D)
x + 20
C
Evaluate the function at the given value of the independent variable and simplify.
146)
f(x) = – 5x + 1;f(–3)
146)
A)
–4
B)
14
C)
16
D)
12
C
Use the given conditions to write an equation for the line in point–slope form.
147)
Passing through (7, 3) and (5, 2)
147)
A)
y – 3 =1
2(x – 5) or y – 2 =1
2(x – 7)
B)
y + 3 =1
2(x + 7) or y + 2 =1
2(x + 5)
C)
y – 3 =1
2(x – 7) or y – 2 =1
2(x – 5)
D)
y – 3 =7(x + 7) or y – 2 =5(x – 3)
C
A
Give the domain and range of the relation.
148)
{(6, 7), (10, –8), (9, 6), (9, 2)}
148)
A)
domain = {9, 6, 10, 19}; range = {6, 7, –8, 2}
B)
domain = {9, 6, 10, –9}; range = {6, 7, –8, 2}
C)
domain = {6, 7, –8, 2}; range = {9, 6, 10}
D)
domain = {9, 6, 10}; range = {6, 7, –8, 2}
Graph the linear function by plotting the x– and y–intercepts.
149)
–5x – 25y –25 = 0
149)
A)
intercepts: (0, –5), (–1, 0)
B)
intercepts: (0, 5), (1, 0)
C)
intercepts: (0, –1), (–5, 0)
D)
intercepts: (0, –1), (5, 0)
C
D
The graph of a function f is given. Use the graph to answer the question.
150)
Find the numbers, if any, at which f has a relative minimum. What are the relative minima?
150)
A)
f has a relative minimum at x = – 2 and 2; the relative minimum is 0
B)
f has a relative minimum at x = – 2; the relative minimum is 0
C)
f has a relative minimum at x = 0; the relative minimum is 3
D)
f has no relative minimum
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
151)
f(x) =2x2, g(x) =2x2–3
151)
76
A)
g shifts the graph of f vertically up 3units
B)
g shifts the graph of f vertically up 3units
C)
g shifts the graph of f vertically down 3units
77
D)
g shifts the graph of f vertically down 3units
Given functions f and g, determine the domain of f +
g.
152)
f(x) =2x – 2,g(x) =2
x +7
152)
A)
(–, )
B)
(0, )
C)
(–, –2) or (–2, )
D)
(–, –7) or (–7, )
D
Find the midpoint of the line segment whose end points are given.
153)
(5, –4) and (7, –1)
153)
A)
(6, –5
2)
B)
(12, –5)
C)
(– 1, –3
2)
D)
(–2, –3)
A
Find the slope of the line that goes through the given points.
154)
(7, –6), (–4, –18)
154)
A)
– 8
B)
–12
11
C)
12
11
D)
11
12
C
D
Find the domain of the composite function f
g.
155)
f(x) = x +5, g(x) =4
x +10
155)
A)
(–, )
B)
(–, –10) or (–10, –5) or (–5, )
C)
(–, –10) or (–10, )
D)
(–, –15) or (–15, )
Use the given conditions to write an equation for the line in the indicated form.
156)
Passing through (5, 3) and perpendicular to the line whose equation is y =1
7x +5;
slope–intercept form
156)
A)
y = – 1
7x –38
7
B)
y = – 7x – 38
C)
y = – 7x + 38
D)
y =7x – 38
C
Solve.
157)
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.
157)
A)
y =48x + 10
B)
y = – 48x +154
C)
y = – 48x –154
D)
y = – 1
48 x +2623
32
B
Use the given conditions to write an equation for the line in the indicated form.
158)
Passing through (3, 2) and parallel to the line whose equation is y =2x – 6;
point–slope form
158)
A)
y –3=2(x – 2)
B)
y – 2 = x –3
C)
y – 2 =2(x –3)
D)
y = 2x
C
C
Identify the intervals where the function is changing as requested.
159)
Increasing
159)
A)
(1, 5)
B)
(1, 6)
C)
(0, 6)
D)
(0, 5)
160)
Increasing
160)
A)
(–2, 2)
B)
(–3, )
C)
(–3, 3)
D)
(–2, )
Begin by graphing the standard cubic function f(x) =x3. Then use transformations of this graph to graph the given
function.
80