Name
Class
Date
Extra Practice
Chapter 2
Lesson 2-1
Determine whether each relation is a function. Justify your answer.
1. {(0, 1), (1, 0), (2, 1), (3, 1), (4, 2)}
Yes; each x-value has exactly one y-value.
3. {(1, 4), (3, 2), (5, 2), (1, 28), (6, 7)}
No; the x-value 1 has two y-values.
5. {(9, 3), (6, 2), (3, 2), (3, 1), (6, 22)}
No; the x-values 3 and 6 have two y-values.
2. {(7, 4), (4, 9), (23, 1), (1, 7), (2, 8)}
Yes; each x-value has exactly one y-value.
4. {(25, 1), (0, 23), (22, 1), (10, 11), (7, 1)}
Yes; each x-value has exactly one y-value.
6. {(4, 9), (5, 3), (22, 0), (5, 4), (8, 1)}
No; the x-value 5 has two y-values.
Evaluate each function for the given value of x, and write the input x and output
f (x) in an ordered pair.
4
2
8. f (x) 5 3x 2 3 for x 5 8 10; (8, 10)
7. f (x) 5 22x 1 11 for x 5 5 1; (5, 1)
9. Make a mapping diagram and a graph for the relation {(1, 3), (22, 2),
(1, 4), (0, 1)}. Then determine whether the relation is a function.
not a function
10. A garden has the shape of an isosceles triangle. The base of the triangle
Domain
Range
-2
1
3
4
-2
0
1
is 42 ft long, with an altitude of h ft. Write an equation that describes the
area A of the garden as a function of h. What is the area of the garden for
h 5 38 ft? A(h) 5 21h; 798 ft2
11. To avoid air turbulence, a plane climbs from an altitude of 20,700 feet
4
y
2
to a higher altitude at the rate of 325 feet per minute. Write a function that
-2 O
describes the altitude, y, of the plane x minutes after it begins its climb.
Then find the altitude of the plane for x 5 5. y 5 20,700 1 325x; 22,325 ft
-2
x
Lesson 2-2
Determine whether y varies directly with x. If so, find the constant of variation.
12. y 5 5x yes; 5
13. y 5 2x 1 2 no
14. 2y 5 27x yes; 272
In Exercises 15–16, y varies directly with x.
15. If y 5 15 when x 5 6, find x when y 5 10.
4
16. If y 5 3 when x 5 2, find y when x 5 25. 215
2
Write an equation of a direct variation that passes through each point.
17. (3, 7) y 5 73x
18. (5, 28) y 5 285x
21. (26, 6) y 5 2x
22. (6, 23) y 5 20.5x 23. (12, 8) y 5 23 x
19. (24, 210) y 5 2.5x 20. (22, 9) y 5 24.5x
1
x
24. (215, 21) y 5 15
25. When a pump is turned on, it pumps water at a rate of 12 gal/min. What
information do you need to know to decide if the volume of water in the
tank varies directly with the time the pump is on? Explain.
You need to know if there was any water in the tank initially.
Prentice Hall Algebra 2 • Extra Practice
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5
Name
Class
Date
Extra Practice (continued)
Chapter 2
Lesson 2-3
Find the slope of the line through each pair of points.
27. (2, 3) and (21, 5) 22
3
26. (1, 5) and (2, 8) 3
28. (3, 1) and (3, 21)
undefined
Write an equation for each line.
2
30. m 5 3 and the y-intercept is 3
y 5 223x 1 3
29. m 5 0 and the y-intercept is 2 y 5 2
Graph each equation.
31. y 5 x 2 7
32. y 5 2x 1 4
y
O
2
4
6
33. y 5 24x 1 3
y
x
y
6
4
-2
2
-4
-2
-6
O
2
x
2
O
-1
4
-2
-8
x
y
34. The blueprint for a toy, shown at the right, identifies two
A (4, 3)
perpendicular rods, each 5 in. long. Suppose each square
in the coordinate grid measures 1 in.2 and the origin is O.
Rods I and II are connected at point (4, 3).
Rod I
Rod II
x
a. Write an equation in slope-intercept form for the line
containing Rod I. y 5 34x
O
b. Write an equation in slope-intercept form for the line
containing Rod II. y 5 43 x 1 25
3
Lesson 2-4
Write in standard form the equation of each line.
35. slope 5 3; (21, 4)
3x 2 y 5 27
2
38. slope 5 25 ; (3, 29)
2x 1 5y 5 239
36. slope 5 21; (0, 7)
x1y57
8
39. slope 5 3 ; (22, 0)
8x 2 3y 5 216
3
37. slope 5 4 ; (2, 8)
3x 2 4y 5 226
40. slope 5 25; (23, 212)
5x 1 y 5 227
Write in point-slope form the equation of the line through each pair of points.
41. (24, 25) and (21, 28)
y 1 5 5 21(x 1 4)
42. (25, 6) and (3, 210)
43. (12, 10) and (0, 0)
y 2 6 5 22(x 1 5)
y 5 56x
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Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
6
Name
Class
Date
Extra Practice (continued)
Chapter 2
Find the slope, y-intercept, and x-intercept of each line.
1
45. y 5 3x 2 15
44. y 5 2x 2 5 2, 25, 2.5
1
3,
215, 45
46. x 5 27
undefined,
none, 27
Write each equation in standard form.
47. 0.3x 1 1.2y 5 2.4
3x 1 12y 5 24
2
48. y 5 3x 1 15
2x 2 3y 5 245
49. x 5 8 2 y
x1y58
51. 22y 5 x 2 2
52. 3x 2 8y 5 9
Graph each equation.
50. 26x 2 2y 5 7
3
y
y
-2
2
-3
1 x
O
-2
O
O
y
x
-2
x
2
-3
Lesson 2-5
53. Make a scatter plot for the following set of points: {(1, 1), (1.5, 1.5),
4
(2, 1), (2.5, 1.5), (3, 2), (3.5, 3), (4, 3), (5, 3), (5.5, 3.5), (6, 4)}. Discuss 2
the correlation. strong, positive correlation
0
2
54. Write the equation of a trend line for the following set of points:
1
{(10, 10), (20, 18), (30, 20), (40, 22)}. Answers will vary. Sample: y 5 5x 1 14
4
6
55. Use a calculator to find the line of best fit for the data in Exercise 54.
y 5 0.38x 1 8; r 5 0.93
How accurate is your line of best fit?
Lesson 2-6
Describe the transformation of parent function f (x).
56. h (x) 5 f (x 2 1)
translation right 1 unit
59. g (x) 5 3.4 f (x) vertical
stretch by a factor of 3.4
57. g (x) 5 f (x) 1 2
translation up 2 units
60. k (x) 5 f (2x)
reflection over y-axis
Describe the transformation of f (x) that produces g (x).
58. k (x) 5 2f (x)
reflection over x-axis
1
61. h(x) 5 2 f (x) vertical
compression by a factor
of 12
62. f (x) 5 2x 2 1 vertical
63. f (x) 5 4x
64. f (x) 5 3x
1
1 vertical
g (x) 5 2 x 1 1 compression g (x) 5 2x 2 2 compression g (x) 5 2(3x 2 1)
by a factor of 14 and
reflected across the y-axis
by a factor of 12 and
and translated up 1 unit
translated up 2 units
translated down 0.5 units
65. The graph of y 5 x is vertically stretched by a factor of 3. It is then translated
up 1 unit. What is the equation for the transformation? y 5 3x 1 1
Prentice Hall Algebra 2 • Extra Practice
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
7
Name
Class
Date
Extra Practice (continued)
Chapter 2
Lesson 2-7
Graph each equation by writing two linear equations.
1
66. y 5 P x 1 2 P
67. y 5 u 4x 1 3 u
y
2
6
1
-1
-2
y
y
6
4
x
O
2
69. y 5 2u x 1 4 u
x
O
-1
-2
-6
68. y 5 u 4x 2 3 u
70. y 5 2 u x 2 3 u
-2
O
y
x
-2
6
x
O
1
2
71. y 5 u x 1 4 u 2 2
y
y
2
4
-4
-6
2
-2
x
x
O
Lesson 2-8
-4
O
2
4
Graph each inequality.
72. y , 2x 1 5
6
73. 0.1x 1 0.6y $ 2
74. y # 3x 2 1
y
y
4
10
2
-10 O
x
O
2
4
2
x
-4
10
-2
O
-10
4
-4
75. x 1 3y . 12
76. y $ 5x 2 3
y
77. 6x 1 2y $ 7
y
y
4
2
-2
O
x
2
4
O
2
x
x
2
O
-4
-2
-2
Prentice Hall Algebra 2 • Extra Practice
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
8
y
2
x
2
4
Overset Text Page 8
y
78. Andrea is going to buy x lbs of pasta salad and y lbs of chicken
salad for a party. The pasta salad costs $4 per pound and the
chicken salad costs $6 per pound. Andrea has at most $28 to
spend. Write and graph an inequality that describes the
relationship between x and y. 4x 1 6y # 28;
6
4
2
O
x
2
4
6