Download 1. Write an inequality that describes the graph. 0 1 2. Use words to

Math 098 Fa2009 Dressler Exam 1 Prepatationv02
1. Write an inequality that describes the graph.
0
1
2. Use words to describe the line graph.
–5
–3
3. Create a line graph of the inequality.
x > –1
4. Write an inequality that describes the graph.
–4
2
5. Write an inequality that describes the graph.
0
2
6. Use words to describe the line graph.
–4
–2
7. Solve the following compound inequality. Write the solution in interval notation.
6 x < 24 and x + 10 > 2
8. Solve the following compound inequality. Write the solution in interval notation.
x + 10 ≥ 19 or 4 x ≤ 20
9. Solve the following compound inequality. Write the solution in interval notation.
–8 x > 32 and x + 3 > 7
Chapter 2
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Math 098 Fa2009 Dressler Exam 1 Prepatationv02
10. Wages The sales agent for a jewelry company is offered a flat monthly salary of $3484
or a salary of $1183 plus 10% commission on the selling price of each item sold by the
agent.
If the agent chooses the $3484, what dollar amount does the agent expect to sell in 1
month?
11. Comparing Services A computer bulletin board service charges a flat fee of $12 per
month or a fee of $4 per month plus $0.16 for each minute the service is used.
How many minutes must a person use this service to exceed $12?
12. Transportation A shuttle service taking skiers to a ski resort charges $9.00 per person
each way. Four skiers are debating whether to take the shuttle bus or rent a car for
$50.00 plus $0.25 per mile.
Assuming that the skiers will share the cost of the car and that they want the least
expensive method of transport, find how far away the ski area is if they choose the
shuttle service.
13. Does the diagram below represent a function?
Chapter 2
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Math 098 Fa2009 Dressler Exam 1 Prepatationv02
14. Does the diagram below represent a function?
15. State whether the following relation is a function.
{(1,3), (2, 6), (3,8), (1, –1), (2, –2)}
16. State whether the following relation is a function.
{(–4,3), (–3,3), (1,3), (3,3), (6,3)}
17. Find the domain and range of the following function.
{(0, 0), (2, 2), (–4, 2), (6, 6), (–5, 6)}
18. Find the range of the function defined by the equation and the given domain.
f ( x) = 3 − 7 x − x 2 ; D = {–2, 0, 2}
19. Given the function f ( x) = 5 x 2 − 4 , find f (2).
20. Given the function s (t ) =
7
, find s (–3).
2t − 4
21. Given the function f ( x) = 2 x 4 − 5 x − 4 , find f (–1).
22. Evaluate the transcript cost function f ( x ) = 8 + 7 ( x − 1) for the specified input.
f (u + v )
Chapter 2
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Math 098 Fa2009 Dressler Exam 1 Prepatationv02
23. Evaluate the transcript cost function f ( x ) = 9 + 7 ( x − 1) for the specified input.
f ( p − q)
24. Evaluate the parabolic function f ( x ) = x 2 + x + 4 for the specified input.
f ( p − q)
25. Evaluate the parabolic function f ( x ) = x 2 + x – 1 for the specified input.
f (t + u )
26. Find the x- and y-intercepts of the line 2 x + 3 y = 18.
27. Find the x- and y-intercepts of the line y = –3 x – 6.
28. Find the x- and y-intercepts and then graph: x – 3 y = 0
29. Use f ( 0 ) to help you find the y-intercept point of the equation.
f ( x) =
4
x–9
7
30. Use f ( x ) = 0 to help you find the x-intercept point of the equation.
f ( x) =
7
x–5
5
31. Find the slope of the line containing the given points.
P1 (–1, 4), P2 (3, –4)
32. Find the slope of the line containing the given points.
P1 (1, –1), P2 (0, 2)
Chapter 2
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Math 098 Fa2009 Dressler Exam 1 Prepatationv02
33. Find the slope of the line containing the given points.
P1 (–2, –2), P2 (0,1)
34. Point (–2, –5) , m = 2.
35. Point (–2, 10) , m = –4.
36. Point (9, –1) , m =
4
.
9
37. Point (–7, –4), slope is undefined.
38. Find the equation of the line that contains the points P1(–6, –3) and P2(8, –3).
39. Find the equation of the line that contains the points P1(–12, –7) and P2(–12, 7).
40. P1 (–1, 2), P2 (1, 6)
41. P1 (2, – 5), P2 (4, –13)
42. P1 (0, 0), P2 (–5, 3)
43. P1 (0, 3), P2 (–5, 7)
44. A Boeing 747 jet takes off from Boston's Logan Airport, which is at sea level, and
climbs to a cruising altitude of 30,000 ft at a constant rate of 1100 ft/min.
a. Write a linear equation for the height of the plane in terms of the time after takeoff.
b. Use your equation to find the height of the plane 24 min after takeoff.
Chapter 2
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Math 098 Fa2009 Dressler Exam 1 Prepatationv02
45. A building contractor estimates that the cost to build a home is $34,000 plus $95 for
each square foot of floor space in the house.
a. Determine a linear function that will give the cost of building a house that contains a
given number of square feet of floor space.
b. Use this model to determine the cost to build a house that contains 1900 square feet
of floor space.
46. A cellular phone company offers several different service plans. One option, for people
who plan on using the phone only in emergencies, costs the user $5.20 per month plus
$0.57 per minute for each minute the phone is used.
a. Write a linear function for the monthly cost of the phone in terms of the number of
minutes the phone is used.
b. Use your equation to find the cost of using the cellular phone for 16 minutes in 1
month.
47. The gas tank of a certain car contains 12 gal of gas when the driver of the car begins a
trip. Each mile driven by the driver decreases the amount of gas in the tank by 0.024
gal.
a. Write a linear function for the number of gallons of gas in the tank in terms of the
number of miles driven.
b. Use your equation to find the number of gallons in the tank after driving 249 mi.
Round your answer to the nearest tenth of a gallon.
48. A manufacturer of graphing calculators has determined that 9000 calculators per week
will be sold at a price of $100 each. At a price of $90, it is estimated that 13,000
calculators would be sold.
a. Determine a linear function that will predict the number of calculators that would be
sold at a given price, x.
b. Use this model to predict the number of calculators that would be sold each week at a
price of $80.
49. Graph by using the slope and y-intercept: y = 3 x – 4
50. Write a linear equation for the following facts:
y-intercept –4, slope 4
Chapter 2
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Math 098 Fa2009 Dressler Exam 1 Prepatationv02
51. Graph by using the slope and y-intercept: y = 3 x – 4
52. Write a linear equation for the following facts:
y-intercept –3, x-intercept –2
53. Find the equation of the line that passes through the following points:
( 0, –1) and (1, –1)
54. Find the equation of the line passing through the given point with the indicated slope.
Point ( 4, –9 ) , zero slope
55. Find the equation of the line passing through the given point with the indicated slope.
Point ( 3, 6 ) , undefined slope
56. Find the equation of the line that passing through the given point with the indicated
slope.
Origin, undefined slope
57. The slope of a line is
5
. What is the slope of any line parallel to this line?
12
58. Is the system parallel, perpendicular, or neither?
y = 5x
4x = y – x – 4
59. The slope of a line is
7
. What is the slope of any line perpendicular to this line?
3
60. Is the system parallel, perpendicular, or neither?
y – 2 x = –9
y = –2 ( x – 3)
61. Find the equation of the line fitting the information given.
Parallel to 5 x – 4 y = –1 and passing through the origin
Chapter 2
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Math 098 Fa2009 Dressler Exam 1 Prepatationv02
62. Find the equation of the line containing the point (6, 1) and perpendicular to the line
y = –5 x + 8 .
63. Find the equation of the line containing the point (8, 29) and perpendicular to the line
10 x + 30 y = –3 .
64. Find the equation of the line containing the point (3, –13) and parallel to the line
6 x + y = –7 .
65. Find the equation of the line fitting the information given.
Perpendicular to –5 x + 2 y = –7 and passing through ( –4, –1)
66. Is x = –6 a solution of the equation | 4 x − 5 | = 29 ?
67. Solve | x | = 9 .
68. Solve | − y | = 6 .
69. Solve | x | = – 7 .
70. Solve | x + 2 | = 8 .
71. Solve | y − 7 | = 10 .
72. Solve | y − 10 | = 0 .
73. Solve | x − 2 | = – 4 .
74. Solve | 4 − 5 x | = 16 .
75. Solve | x − 3 | −3 = 6 .
Chapter 2
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Math 098 Fa2009 Dressler Exam 1 Prepatationv02
76. Solve | 7 a + 2 | −8 = 8 .
77. Solve |10 x − 4 | −3 = 6 .
78. Solve 12 − | 2 x − 5 | = 7 .
79. Solve | 6 − 5 x | +3 = 9 .
80. Solve 8 − | 9 x + 5 | = 5 .
Chapter 2
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Math 098 Fa2009 Dressler Exam 1 Prepatationv02
Answer Key
1. x < 1
2. x is between –5 and –3, including –5 and –3
3.
–1
4. –4 < x < 2
5. x < 0 or x > 2
6. x is less than –4 or greater than –2
7. (–8, 4)
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
( −∞,5] ∪ [9, ∞ )
∅
≤ $23, 010
> 50 min
> 44 mi
Yes
No
Not a function
Function
D: {–5, –4, 0, 2, 6}; R: {0, 2, 6}
{13, 3, –15}
16
7
–
10
3
7u + 7v + 1
7 p – 7q + 2
24. p 2 – 2pq + q 2 + p – q + 4
25.
26.
27.
t 2 + 2tu + u 2 + t + u – 1
x-intercept: (9, 0), y-intercept: (0, 6)
x-intercept: (–2, 0), y-intercept: (0, –6)
Chapter 2
Page 10
0
Math 098 Fa2009 Dressler Exam 1 Prepatationv02
28. x-intercept: (0, 0), y-intercept: (0, 0)
29.
( 0, –9 )
⎛ 25 ⎞
30. ⎜ , 0 ⎟
⎝ 7
⎠
31. –2
32. –3
3
33.
2
34. y = 2 x –1
35. y = –4 x + 2
4
36. y = x – 5
9
37. x = –7
38. y = –3
39. x = –12
40. y = 2 x + 4
41. y = –4 x + 3
3
42. y = – x
5
4
43. y = – x + 3
5
3
; (b) 26,400 ft
11
y = 95 x + 34, 000 ; (b) $214,500
y = 0.57 x + 5.20 ; (b) $14.32
y = –0.024 x + 12, 0 ≤ x ≤ 499 ; (b) 6.0 gal
y = –400 x + 49000 ; (b) 17,000 calculators
44. (a) y = 1100 x, 0 ≤ x ≤ 27
45.
46.
47.
48.
(a)
(a)
(a)
(a)
Chapter 2
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Math 098 Fa2009 Dressler Exam 1 Prepatationv02
49.
50. y = 4 x – 4
51.
3
x–3
2
y = –1
y = –9
x=3
x=0
5
12
parallel
3
−
7
neither
5
y= x
4
52. y = –
53.
54.
55.
56.
57.
58.
59.
60.
61.
Chapter 2
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Math 098 Fa2009 Dressler Exam 1 Prepatationv02
1
1
x−
5
5
y = 3x + 5
y = –6 x + 5
2
13
y=– x–
5
5
Yes
Both A and B
Both B and C
No solution
Both A and B
Both B and C
10
No solution
Both A and B
Both B and C
Both A and C
Both A and B
Both A and B
Both B and C
Both A and C
62. y =
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
Chapter 2
Page 13