39
CHAPTER 2, FORM A
COLLEGE ALGEBRA
NAME
DATE
1. Match the set described in Column I with the correct interval 1. a. _____________
notation from Column II. Choices in Column II may be used
once, more than once, or not at all. b. _____________
I II c. _____________
a. Domain of
( ) 3f x x=−
A.
( , )−
d. _____________
b. Range of
( ) 3f x x=−
B.
)
3,
c. Domain of
( )
216f x x=−
C.
0, 2
e. _____________
d. Range of
2
2yx=
D.
)
0,
e. Domain of
3
( ) 2f x x=−
E.
3,3−
f. _____________
f. Range of
3
( ) 2f x x=+
F.
(
,2− −
g. Domain of
( ) 2f x x=+
G.
)
3,−
g. _____________
h. Range of
( ) 3f x x=+
H.
)
7,−
i. Domain of
2
2ys=
h. _____________
j. Range of
( )
27f x x=−
i. _____________
j. _____________
The graph shows the line that passes through the points (
−
5,
−
3)
and (
−
1, 4). Refer to it to answer Exercises 2–6.
2. What is the slope of the line? 2. ___________________________
3. What is the distance between the two points shown? 3. ___________________________
4. What are the coordinates of the midpoint of the segment 4. ___________________________
joining the two points?
5. Find the standard form of the equation of the line. 5. ___________________________
6. Write the linear function defined by
()f x ax b=+
that 6. ___________________________
has this line as its graph.
40
CHAPTER 2, FORM A
Tell whether each graph is that of a function. Give the domain and the range. If it is a function, give the intervals
where it is increasing, decreasing, or constant.
7.
7. ___________________________
___________________________
___________________________
___________________________
___________________________
8.
8. ___________________________
___________________________
___________________________
___________________________
___________________________
9. Suppose point P has coordinates
23
,.
57
a. What is the equation of the vertical line through P? 9. a. __________________________
b. What is the equation of the horizontal line through P? b. __________________________
10. Find the slope-intercept form of the equation of the line passing
through (2, 5) and
a. parallel to the graph of
4 7;yx=−
10. a. __________________________
b. perpendicular to the graph of
4 7.yx=−
b. __________________________
Graph each relation.
11.
2 3 1xy= − +
11.
41
CHAPTER 2, FORM A
12.
( )
2f x x=+
12.
13.
( )
2 1 if 0
3 1 if 0
xx
fx xx
−
=− −
13.
14. Explain how the graph of
135
2
yx= − + +
can be obtained 14. ___________________________
from the graph of
.yx=
15. Determine whether the graph of
22
2 3 1xy+=
is symmetric 15. a. _________________________
with respect to b. _________________________
a. the x-axis, c. _________________________
b. the y-axis,
c. the origin.
Given
( )
21f x x=−
and
( )
2 1,g x x=+
find each of the following. Simplify the expressions when possible.
16.
()
( )
fg x
16. ___________________________
17.
()
( )
f g x+
17. ___________________________
18. the domain of
g
f
18. ___________________________
42
CHAPTER 2, FORM A
19.
( ) ( )
f x h f x
h
+−
19. ___________________________
20.
()
( )
0fg−
20. ___________________________
21.
( )
2
f
g
21. ___________________________
22.
()
( )
f g x
22. ___________________________
23.
()
( )
2fg−
23. ___________________________
24.
()
( )
g f x
24. ___________________________
25.
()
( )
2gf−
25. ___________________________
43
CHAPTER 2, FORM B
COLLEGE ALGEBRA
NAME
DATE
1. Match the set described in Column I with the correct interval 1. a. _____________
notation from Column II. Choices in Column II may be used
once, more than once, or not at all. b. _____________
I II c. _____________
a. Domain of
( ) 4f x x=−
A.
( , )−
d. _____________
b. Range of
( ) 2f x x=−
B.
)
2,−
c. Domain of
( )
2
3f x x=
C.
0, 2
e. _____________
d. Range of
( )
25f x x=+
D.
)
0,
e. Domain of
3
( ) 8f x x=−
E.
3,3−
f. _____________
f. Range of
3
( ) 1f x x=−
F.
(
,2− −
g. Domain of
( ) 2f x x=−
G.
)
5,
g. _____________
h. Range of
( ) 5f x x=+
H.
)
4,
i. Domain of
2
2xy=
h. _____________
j. Range of
2
2xy=
i. _____________
j. _____________
The graph shows the line that passes through the points (
−
2,
−
1)
and (4,
−
3). Refer to it to answer Exercises 2–6.
2. What is the slope of the line? 2. ___________________________
3. What is the distance between the two points shown? 3. ___________________________
4. What are the coordinates of the midpoint of the segment 4. ___________________________
joining the two points?
5. Find the standard form of the equation of the line. 5. ___________________________
6. Write the linear function defined by
()f x ax b=+
that 6. ___________________________
has this line as its graph.
44
CHAPTER 2, FORM B
Tell whether each graph is that of a function. Give the domain and the range. If it is a function, give the intervals
where it is increasing, decreasing, or constant.
7.
7. ___________________________
___________________________
___________________________
___________________________
___________________________
8.
8. ___________________________
___________________________
___________________________
___________________________
___________________________
Graph each relation.
9.
( )
23f x x=−
9.
10.
( )
1
2
f x x=
10.
45
CHAPTER 2, FORM B
11.
( )
2 if 3
4 if 3 2
4 if 2
xx
f x x
xx
− −
= −
−
11.
12. Suppose point P has coordinates
57
,.
89
−
a. What is the equation of the vertical line through P? 12. a. __________________________
b. What is the equation of the horizontal line through P? b. __________________________
13. Find the slope-intercept form of the equation of the line passing
through
()
6,3−
and
a. parallel to the graph of
3 12;yx= − −
13. a. __________________________
b. perpendicular to the graph of
3 12.yx= − −
b. __________________________
14. Explain how the graph of
142
3
yx= − + +
can be obtained 14. ___________________________
from the graph of
.yx=
15. Determine whether the graph of
23yx=
is symmetric 15. a. _________________________
with respect to b. _________________________
a. the x-axis, c. _________________________
b. the y-axis,
c. the origin.
Given
( )
2
2 7 6f x x x= + +
and
( )
3 2,g x x=−
find each of the following. Simplify the expressions when possible.
16.
()
( )
fg x
16. ___________________________
17.
()
( )
f g x−
17. ___________________________
18. the domain of
g
f
18. ___________________________
46
CHAPTER 2, FORM B
19.
( ) ( )
f x h f x
h
+−
19. ___________________________
20.
( )
( )
1fg+
20. ___________________________
21.
( )
0
g
f
21. ___________________________
22.
()
( )
f g x
22. ___________________________
23.
()
( )
1fg
23. ___________________________
24.
()
( )
g f x
24. ___________________________
25.
()
( )
1gf
25. ___________________________
47
CHAPTER 2, FORM C
COLLEGE ALGEBRA
NAME
DATE
1. Match the set described in Column I with the correct interval 1. a. _____________
notation from Column II. Choices in Column II may be used
once, more than once, or not at all. b. _____________
I II c. _____________
a. Domain of
( ) 2f x x=+
A.
( , )−
d. _____________
b. Range of
( ) 4f x x=−
B.
)
4,−
c. Domain of
( )
21f x x=−
C.
0, 2
e. _____________
d. Range of
( )
216f x x=−
D.
)
0,
e. Domain of
3
( ) 2f x x=−
E.
3,3−
f. _____________
f. Range of
3
( ) 2f x x=+
F.
(
,3− −
g. Domain of
( ) 3f x x=+
G.
)
1,−
g. _____________
h. Range of
( ) 3f x x=−
H.
)
2,−
i. Domain of
2
2yx=
h. _____________
j. Range of
23yx=−
i. _____________
j. _____________
The graph shows the line that passes through the points (
−
3,
−
5)
and (3,
−
2). Refer to it to answer Exercises 2–6.
2. What is the slope of the line? 2. ___________________________
3. What is the distance between the two points shown? 3. ___________________________
4. What are the coordinates of the midpoint of the segment 4. ___________________________
joining the two points?
5. Find the standard form of the equation of the line. 5. ___________________________
6. Write the linear function defined by
()f x ax b=+
that 6. ___________________________
has this line as its graph.
48
CHAPTER 2, FORM C
Tell whether each graph is that of a function. Give the domain and the range. If it is a function, give the intervals
where it is increasing, decreasing, or constant.
7.
7. ___________________________
___________________________
___________________________
___________________________
___________________________
8.
8. ___________________________
___________________________
___________________________
___________________________
___________________________
9. Suppose point P has coordinates
( )
2 2, 5 .−
a. What is the equation of the vertical line through P? 9. a. __________________________
b. What is the equation of the horizontal line through P? b. __________________________
10. Find the slope-intercept form of the equation of the line passing
through (4,
2−
) and
a. parallel to the graph of
52;
4
xy=−
10. a. __________________________
b. perpendicular to the graph of
52;
4
xy=−
b. __________________________
49
CHAPTER 2, FORM C
Graph each relation.
11.
( )
112
2
f x x= + −
11.
CHAPTER 2, FORM A
12.
( )
22f x x=−
12.
13.
( )
1 if 2
1 if 2
xx
fx x
+ −
=− −
13.
50
CHAPTER 2, FORM C
14. Explain how the graph of
3 4 2yx= + +
can be obtained 14. ___________________________
from the graph of
.yx=
15. Determine whether the graph of
2
37yx=+
is symmetric 15. a. _________________________
with respect to b. _________________________
a. the x-axis, c. _________________________
b. the y-axis,
c. the origin.
Given
( )
2
32f x x=−
and
( )
4 4,g x x=+
find each of the following. Simplify the expressions when possible.
16.
()
( )
fg x
16. ___________________________
17.
()
( )
g f x−
17. ___________________________
18.
( 2)f−
18. ___________________________
19.
( ) ( )
f x h f x
h
+−
19. ___________________________
20.
()
( )
0fg+
20. ___________________________
21.
( )
2
f
g
−
21. ___________________________
22.
()
( )
f g x−
22. ___________________________
23.
()
( )
f g x
23. ___________________________
24.
()
( )
g f x
24. ___________________________
25.
( )
( )
0gf
25. ___________________________
51
CHAPTER 2, FORM D
COLLEGE ALGEBRA
NAME
DATE
1. Match the set described in Column I with the correct interval 1. a. _____________
notation from Column II. Choices in Column II may be used
once, more than once, or not at all. b. _____________
I II c. _____________
a. Domain of
( ) 1f x x=+
A.
(
,1− −
d. _____________
b. Range of
( ) 1f x x=+
B.
()
,−
c. Domain of
( )
225f x x=−
C.
0, 2
e. _____________
d. Range of
( )
21f x x=−
D.
)
0,
e. Domain of
3
( ) 2f x x=−
E.
3,3−
f. _____________
f. Range of
3
( ) 2f x x=+
F.
)
3,−
g. Domain of
( ) 4f x x=+
G.
)
1,−
g. _____________
h. Range of
( ) 4f x x=−
H.
)
4,−
i. Domain of
2
2yx=
h. _____________
j. Range of
24yx=−
i. _____________
j. _____________
The graph shows the line that passes through the points (
−
7,
−
4)
and (3,
−
2). Refer to it to answer Exercises 2–6.
2. What is the slope of the line? 2. ___________________________
3. What is the distance between the two points shown? 3. ___________________________
4. What are the coordinates of the midpoint of the segment 4. ___________________________
joining the two points?
5. Find the standard form of the equation of the line. 5. ___________________________
6. Write the linear function defined by
()f x ax b=+
that 6. ___________________________
has this line as its graph.
52
CHAPTER 2, FORM D
Tell whether each graph is that of a function. Give the domain and the range. If it is a function, give the intervals
where it is increasing, decreasing, or constant.
7.
7. ___________________________
___________________________
___________________________
___________________________
___________________________
8.
8. ___________________________
___________________________
___________________________
___________________________
___________________________
Graph each relation.
9.
( )
31f x x= + +
9.
10.
( )
if 0
2 if 0
xx
fx xx
−
=
10.
53
CHAPTER 2, FORM D
11. Suppose point P has coordinates
( )
3,2.1 .−
a. What is the equation of the vertical line through P? 11. a. __________________________
b. What is the equation of the horizontal line through P? b. __________________________
12. Find the slope-intercept form of the equation of the line passing
through (1,
5−
) and
a. parallel to the graph of
35;
4
xy= − +
12. a. __________________________
b. perpendicular to the graph of
35;
4
xy= − +
b. __________________________
13. Find the slope of the line through points (11,
5−
) and (
8−
, 6). 13. ___________________________
from the graph of
.yx=
14. Explain how the graph of
3 4 2yx= − −
can be obtained 14. ___________________________
from the graph of
.yx=
15. Determine whether the graph of
4xy =−
is symmetric 15. a. _________________________
with respect to b. _________________________
a. the x-axis, c. _________________________
b. the y-axis,
c. the origin.
Given
( )
3
2 3 1f x x x= − −
and
( )
2 1,g x x=+
find each of the following. Simplify the expressions when possible.
16.
()
( )
f g x+
16. ___________________________
17.
( )
fx
g
17. ___________________________
18.
( )
0f
18. ___________________________
19.
( ) ( )
f x h f x
h
+−
19. ___________________________
20.
()
( )
0gf−
20. ___________________________
21.
()
( )
1fg −
21. ___________________________
22.
()
( )
f g x
22. ___________________________
54
CHAPTER 2, FORM D
23.
()
( )
2fg
23. ___________________________
24.
()
( )
g f x
24. ___________________________
25.
()
( )
2gf
25. ___________________________
55
CHAPTER 2, FORM E
COLLEGE ALGEBRA
NAME
DATE
Choose the best answer.
1a. Which of the following is the domain of
( )
3?f x x=−
1a. __________________
a.
0,3
b.
(
,3−
c.
)
3,
d.
()
,−
1b. Which of the following is the range of
( )
249?f x x=−
1b. __________________
a.
)
49,−
b.
)
7,−
c.
7,7−
d.
)
0,
1c. Which of the following is the domain of
( )
37?f x x=+
1c. __________________
a.
()
,−
b.
(
,6−
c.
)
0,
d.
)
6,
1d. Which of the following is the range of
( )
1?f x x=+
1d. _________________
a.
1,1−
b.
0,1
c.
)
0,
d.
)
1,
1e. Which of the following is the domain of
2?xy=
1e. __________________
a.
()
,−
b.
)
0,
c.
()
0,
d.
(
,0−
The graph shows the line that passes through
()
5,8−
and
()
4, 3−
. Refer to it to
answer Exercises 2-6.
2. What is the slope of the line? 2. ___________________
a.
13
7
−
b.
11
9
c.
11
9
−
d.
0
3. What is the distance between the two points shown? 3. ___________________
a.
26
b.
25
c.
202
d.
122
56
CHAPTER 2, FORM E
4. What are the coordinates of the midpoint of the segment joining 4. ___________________
the two points?
a.
15
,
22
−
b.
9 11
,
22
−
c.
31
,
22
d.
()
1,5−
5. Find the standard form of the equation of the line. 5. ___________________
a.
11 9 127xy+=
b.
11 9 17xy−=
c.
11 9 17xy+=
d.
11 9 127xy−=
6. Find the standard form of the equation of the line. 6. ___________________
a.
( )
11 17
99
f x x=−
b.
( )
11 17
99
f x x= − +
c.
( )
11 127
99
f x x=+
d.
( )
11 127
99
f x x=−
Tell whether each graph is that of a function. Give the domain and range.
7.
7. ___________________
a. Function; domain:
5,7−
; range:
1,3−
b. Function; domain:
()
,−
; range:
1,3−
c. Function; domain:
1,3−
; range:
5,7−
d. Not a function; domain:
5,7−
; range:
1,3−
8.
8. ___________________
a. Not a function; domain:
()
,−
; range:
)
2,−
b. Not a function; domain:
5,5−
; range:
)
3,−
c. Function; domain:
()
,−
; range:
)
2,−
d. Function; domain:
()
,−
; range:
)
3,−
57
CHAPTER 2, FORM E
9. Suppose point P has coordinates
()
6,1−
. 9. ___________________
What is the equation of the horizontal line through P?
a.
6x=−
b.
1y=
c.
1x=
d.
6y=
10. Find the slope-intercept form of the equation of the line passing. 10. __________________
through
()
2,5−
perpendicular to the graph of
1 19 .
84
yx= − +
a.
8 21yx=+
b.
13
3
yx=−
c.
8 13yx= − −
d.
13
3
yx= − +
Graph each function.
11.
( )
2 1 2f x x= − −
11. __________________
a. b.
c. d.
58
CHAPTER 2, FORM E
12.
( )
1
2
f x x=
12. __________________
a. b.
c. d.
13.
( )
2 if 2
11 if 2
2
x
fx xx
−
=− + −
13. __________________
a. b.
c. d.
59
CHAPTER 2, FORM E
14. Explain how the graph of
25yx= + −
can be obtained from the 14. __________________
graph of
.yx=
a. Translate 2 unit to the right and 5 units up.
b. Translate 2 unit to the right and 5 units down.
c. Translate 2 unit to the left and 5 units up.
d. Translate 2 unit to the left and 5 units down.
15. Determine the symmetries of the graph of the relation
22
2 5.x xy y− + =
15. __________________
a. x-axis only b. y-axis only
c. origin only d. x-axis, y–axis, and origin
Given
( )
54f x x=−
and
( )
23,g x x=+
find each of the following.
Simplify the expressions when possible.
16.
()
( )
fg x
16. __________________
a.
32
4 12xx+−
b.
32
5 4 15 12x x x− + −
c.
32
5 4 3 12x x x+ + −
d.
32
5 4 5 12x x x− + − −
17.
()
( )
g f x−
17. __________________
a.
257xx−+
b.
257xx+−
c.
251xx− − +
d.
251xx++
18. The domain of
g
f
18. __________________
a.
44
,,
55
−
b.
55
,,
44
−
c.
11
,,
33
−
d.
()
,−
19.
( ) ( )
f x h f x
h
+−
19. __________________
a.
h
b.
5
c.
52xh+
d.
5 2 4xh+−
20.
()
( )
1fg+−
20. __________________
a.
1−
b.
5−
c.
2
d.
5
60
CHAPTER 2, FORM E
21.
( )
0
f
g
21. __________________
a.
3
4
−
b.
1
4
c.
4
3
−
d.
15
2
22.
()
( )
g f x
22. __________________
a.
2
25 40 19xx+−
b.
2
25 40 19xx−+
c.
2
25 40 19xx−−
d.
2
25 40 19xx++
23.
()
( )
1gf
22. __________________
a.
6−
b.
4
c.
0
d.
1
24.
()
( )
f g x
24. __________________
a.
2
5 11x−
b.
2
5 11x+
c.
2
5 19x+
d.
2
5 12x−
25.
( )
( )
0fg
25. __________________
a.
1−
b.
0
c.
11
d.
15
61
CHAPTER 2, FORM F
COLLEGE ALGEBRA
NAME
DATE
Choose the best answer.
1a. Which of the following is the domain of
( )
1?f x x=−
1a. __________________
a.
0,1
b.
(
,1−
c.
)
1,
d.
()
,−
1b. Which of the following is the range of
( )
24?f x x=−
1b. __________________
a.
)
2,−
b.
)
4,−
c.
4, 4−
d.
)
0,
1c. Which of the following is the domain of
( )
37?f x x=−
1c. __________________
a.
()
,−
b.
(
,3−
c.
)
0,
d.
)
3,
1d. Which of the following is the range of
( )
2?f x x=+
1d. _________________
a.
2, 2−
b.
0, 2
c.
)
2,
d.
)
0,
1e. Which of the following is the domain of
2?xy=
1e. __________________
a.
()
,−
b.
)
0,
c.
()
0,
d.
(
,0−
The graph shows the line that passes through
()
7, 4−−
and
()
3, 2−
. Refer to it to
answer Exercises 2-6.
2. What is the slope of the line? 2. ___________________
a.
0
b.
1
5
−
c.
1
5
d.
5
3. What is the distance between the two points shown? 3. ___________________
a.
122
b.
2 26
c.
2 13
d.
2 34
62
CHAPTER 2, FORM F
4. What are the coordinates of the midpoint of the segment joining 4. ___________________
the two points?
a.
1 11
,
22
−
b.
()
2, 1−−
c.
()
5, 1−−
d.
()
2, 3−−
5. Find the standard form of the equation of the line. 5. ___________________
a.
5 17xy−=
b.
5 17xy+ = −
c.
5 13xy−=
d.
5 13xy+ = −
6. Find the standard form of the equation of the line. 6. ___________________
a.
( )
1 13
55
f x x=−
b.
( )
5 17f x x= − +
c.
( )
5 17f x x=−
d.
( )
1 13
55
f x x=+
Tell whether each graph is that of a function. Give the domain and range.
7.
7. ___________________
a. not a function; domain:
()()
,0 0,−
; range:
(
()
, 2 0,− −
b. not a function; domain:
()
,−
; range:
()
,−
c. not a function; domain:
()()
,0 0,−
; range:
()
,−
d. not a function; domain:
()()
,0 0,−
; range:
(
()
, 2 2,− −
8.
8. ___________________
a. not a function; domain:
2,1−
; range:
()
,−
b. not a function; domain:
7,5−
; range:
2,1−
c. not a function; domain:
7,5−
; range:
()
,−
d. not a function; domain:
2,1−
; range:
7,5−
63
CHAPTER 2, FORM F
9. Suppose point P has coordinates
()
3,6−
. 9. ___________________
What is the equation of the horizontal line through P?
a.
3x=−
b.
3y=−
c.
6x=
d.
6y=
10. Find the slope-intercept form of the equation of the line passing. 10. __________________
through
()
1, 2
perpendicular to the graph of
11
.
83
yx= − +
a.
83yx=−
b.
11
83
yx=−
c.
83yx= − +
d.
1 17
88
yx= − +
Graph each relation.
11.
( )
11
2
f x x=+
11. __________________
a. b.
c. d.
64
CHAPTER 2, FORM F
12.
( )
12
2
f x x=−
12. __________________
a. b.
c. d.
13.
( )
2 if 1
3 if 1
xx
fx xx
− −
=+ −
13. __________________
a. b.
c. d.
14. Explain how the graph of
31yx= + +
can be obtained from the 14. __________________
graph of
.yx=
a. Translate 3 units to the right and 1 units up.
b. Translate 3 units to the right and 1 units down.
c. Translate 3 units to the left and 1 units up.
d. Translate 3 units to the left and 1 units down.
65
CHAPTER 2, FORM F
15. Determine the symmetries of the graph of the relation
22
4 9 36.xy+=
15. __________________
a. x-axis only b. y-axis only
c. Origin only d. x-axis, y-axis, and origin
Given
( )
2
6 5 6f x x x= + −
and
( )
2 8,g x x=−
find each of the following.
Simplify the expressions when possible.
16.
( )
3f−
16. __________________
a.
9−
b.
21
c.
33
d.
51
17.
( ) ( )
f x h f x
h
+−
17. __________________
a.
12 6 5xh++
b.
12 6 5xh−−
c.
12 6 5xh− = +
d.
12 6 5xh− + −
18.
()
3
2
fg
18. __________________
a.
131−
b.
119
c.
181−
d.
169
19.
( )
( )
f g x+
19. __________________
a.
2
6 7 14xx+−
b.
2
6 7 14xx−−
c.
2
6 7 2xx+−
d.
2
6 3 2xx−−
20.
( )
( )
0fg+
20. __________________
a.
15−
b.
14−
c.
27−
d.
1
66
CHAPTER 2, FORM A
67
68
CHAPTER 2, FORM B
69
CHAPTER 2, FORM C
70
71
72
CHAPTER 2, FORM D
73
74
CHAPTER 2, FORM E
75
CHAPTER 2 FORM F