7/27/2019 tcu11_01pr

1/2

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

Copyright 2005 Pearson Education, Inc., publishing as Pearson Addison-Wesley

7/27/2019 tcu11_01pr

2/2

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

Copyright 2005 Pearson Education, Inc., publishing as Pearson Addison-Wesley