tcu11_01pr
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Chapter 1 Practice Exercises 69
Chapter1 Practice Exercises
InequalitiesIn Exercises 14, solve the inequalities and show the solution sets on
the real line.
1. 2.
3. 4.
Absolute Value
Solve the equations or inequalities in Exercises 58.
5. 6.
7. 8.
Coordinates
9. A particle in the plane moved from to they-axis in such
a way that equaled What were the particles new coordi-
nates?10. a. Plot the points and
E( , 6).
b. Find the slopes of the lines AB, BC, CD, DA, CE, andBD.
c. Do any four of the five points A, B, C, D, andEform a paral-
lelogram?
d. Are any three of the f ive points collinear? How do you know?
e. Which of the lines determined by the f ive points pass through
the origin?
11. Do the points and form an isosceles
triangle? A right triangle? How do you know?
12. Find the coordinates of the point on the line that is
equidistant from (0, 0) and
LinesIn Exercises 1324, write an equation for the specified line.
13. through with slope 3
14. through with slope
15. the vertical line through s0, -3d
-1>2s -1, 2ds1, -6d
s -3, 4d .y = 3x + 1
Cs -2, 3dAs6, 4d, Bs4, -3d ,
14>3 Ds2, -3d ,Cs -4, 6d,Bs2, 10d,As8, 1d,3x .y
As -2, 5d
` 2x + 73
` 5` 1 - x2
` 7 32
y - 3 6 4x + 1 = 7
x - 32
-4 + x
315
sx - 1d 614
sx - 2d
-3x 6 107 + 2x 3
16. through and
17. the horizontal line through (0, 2)
18. through (3, 3) and
19. with slope andy-intercept 3
20. through (3, 1) and parallel to
21. through and parallel to
22. through and perpendicular to
23. through and perpendicular to
24. with x-intercept 3 andy-intercept
Functions and Graphs
25. Express the area and circumference of a circle as functions of the
circles radius. Then express the area as a function of the circum-
ference.
26. Express the radius of a sphere as a function of the spheres surface
area. Then express the surface area as a function of the volume.27. A point P in the first quadrant lies on the parabola Ex-
press the coordinates ofPas functions of the angle of inclination
of the line joining Pto the origin.
28. A hot-air balloon rising straight up from a level field is tracked by
a range finder located 500 ft from the point of liftoff. Express the
balloons height as a function of the angle the line from the range
finder to the balloon makes with the ground.
In Exercises 2932, determine whether the graph of the function is
symmetric about the y-axis, the origin, or neither.
29. 30.
31. 32.
In Exercises 3340, determine whether the function is even, odd, or
neither.
33. 34.
35. 36.
37. 38.
39. 40. y = 2x4 - 1y = x + cosx
y = 1 - sinxy = x
4 +1
x3 - 2x
y = secxtanxy = 1 - cosx
y = x5 - x3 - xy = x2 + 1
y = e-x2
y = x2 - 2x - 1
y = x2>5y = x1>5
y = x2 .
-5
s1
>2dx + s1
>3dy = 1s -1, 2d
3x - 5y = 1s -2, -3d
4x + 3y = 12s4, -12d
2x - y = -2
-3
s -2, 5d
s1, -2ds -3, 6d
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In Exercises 4150, find the (a) domain and(b) range.
41. 42.
43. 44.45. 46.
47. 48.
49. 50.
Piecewise-Defined FunctionsIn Exercises 51 and 52, find the (a) domain and(b) range.
51.
52.
In Exercises 53 and 54, write a piecewise formula for the function.
53. 54.
Composition of FunctionsIn Exercises 55 and 56, find
a. b.
c. d.
55.
56.
In Exercises 57 and 58, (a) write a formula for and and
find the (b) domain and(c) range of each.
57.
58.
Composition with absolute values In Exercises 5964, graphand together. Then describe how applying the absolute value func-
tion before applying affects the graph.
59. x
60.
61.
62.
63.
64. sinx sin x
2x 2x
1
x
1x
x 2x2x 3x3x
2sxd 1s x d1sxd
1
21
sxd = 2x,gsxd = 21 - xsxd = 2 - x2,gsxd = 2x + 2 g gsxd = 2 - x,gsxd = 23 x + 1sxd =
1x ,gsxd = 12x + 2 sg gdsxd .s dsxd .
sg ds2d .s gds -1d .
x
5(2, 5)
0 4
y
x
1
10 2
y
y = -x - 2, -2 x -1 x, -1 6 x 1-x + 2, 1 6 x 2
y =
e2-x, -4 x 0
2x, 0
6x
4
y = -1 + 23 2 - xy = lnsx - 3d + 1
y = x2>5y = 2sins3x + pd - 1y = tans2x - pdy = 2e-x - 3y = 3
2 -x
+ 1y = 216 - x2
y = -2 + 21 - xy = x - 2
Composition with absolute values In Exercises 6568, graph
and together. Then describe how taking absolute values after apply-
ing affects the graph.
65.
66.
67.
68.
Trigonometry
In Exercises 6972, sketch the graph of the given function. What is theperiod of the function?
69. 70.
71. 72.
73. Sketch the graph
74. Sketch the graph
In Exercises 7578, ABC is a right triangle with the right angle at C.
The sides opposite angles A, B, andCare a, b, andc, respectively.
75. a. Finda andb if
b. Finda andc if
76. a. Express a in terms ofA andc.
b. Express a in terms ofA andb.
77. a. Express a in terms ofB andb.
b. Express c in terms ofA anda.
78. a. Express sin A in terms ofa andc.
b. Express sin A in terms ofb andc.
79. Height of a pole Two wires stretch from the top Tof a vertical
pole to points B andCon the ground, where C is 10 m closer to
the base of the pole than is B. If wire BTmakes an angle of 35
with the horizontal and wire CTmakes an angle of 50 with the
horizontal, how high is the pole?80. Height of a weather balloon Observers at positions A andB
2 km apart simultaneously measure the angle of elevation of a
weather balloon to be 40 and 70, respectively. If the balloon is
directly above a point on the line segment between A andB, find
the height of the balloon.
81. a. Graph the function
b. What appears to be the period of this function?
c. Confirm your finding in part (b) algebraically.
82. a. Graph
b. What are the domain and range of ?
c. Is periodic? Give reasons for your answer.
sxd = sins1>xd .sxd = sinx + cossx>2d .
b = 2, B = p>3.c = 2, B = p>3.
y = 1 + sin ax +p
4 b .y = 2cos ax - p
3b .
y = cospx
2y = sinpx
y = sinx
2y = cos2x
x2 + x x2 + x
4 - x2 4 - x2 2x 2x
x3 x3g2sxd g1sxd g1sxd
g1
g2
g1
70 Chapter 1: Preliminaries
T
T
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