Solution manual for precalculus 1st edition by miller

No vertical line intersects the graph in more than one point.. No vertical line intersects the graph in more than one point.. There is at least one vertical line that intersects the g

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Chapter 1 Functions and Relations Section 1.1 The Rectangular Coordinate System and Graphing Utilities

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b

1 2 1 2,

6.4 2.45.2 2.2

,

7.4 8.8, 3.7, 4.4

32.7 24.731.1 37.1

,

68.2 57.4, 34.1, 28.7

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Yes

b

( ) ( )

2 2

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− ≠

≠{x x| ≠3}

26 7 0

7

x x

+ ≠

≠ −

{x x| ≠ −7}

27 10 0

10

x x

− ≥

≥

{x x| ≥10}

28 11 0

11

x x

+ ≥

≥ −

{x x| ≥ −11}

29 1.5 0

1.51.5

x x x

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− −2

1

212

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7 ±3 y= ± ( )7 + = ±2 3 ( ) ( )7,3 , 7, 3 −

40 2

2

1 011

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45 x-intercepts: ( ) ( )−1,0 , 9,0

y-intercepts: ( ) ( )0, 3 , 0,3−

46 x-intercepts: (−16,0 , 4,0) ( )

y-intercepts: ( ) ( )0, 8 , 0,8−

47 x-intercept: ( )−2,0 ; y-intercept: none

48 x-intercept: none; y-intercept: ( )0,1

x y x x x

x y y y y

x y x x x

x y y y y

9

93

x y x x x

9

x y y y

+ =+ =

16

0 1616

4

x x x

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= + −

= + −+ =

1

x y x

1

11

x y y y y

4

x y x x

4

42

x y y y y

x y x x

x y y y

x x x

x y y y

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2 2 2

9283

9

x

x x x x x

4454

4

y y y y y y

Not a real number

x-intercept: none; y-intercept: none

2 2

= − ± − Not a real number

x-intercept: none; y-intercept: none

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b If both the player move directly

towards each other at the same speed, then they will meet at the midpoint

meet at the midpoint of (223,184)

( ) ( ) (2 )2, 120 80 60 210

Therefore, the points A, B, and C

make up the vertices of an equilateral triangle

68 ( ) ( ) (2 )2

d A B = x− + − = x ( ) ( ) (2 )2

d A C = − + x− = x

make up the vertices of an isosceles triangle

make up the vertices of an isosceles right triangle

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 − −  + −

= =+

2 23,12

 − −  + − −

= =+

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79 The points (x y1, 1) and (x2,y2)

define the endpoints of the

hypotenuse d of a right triangle The

lengths of the legs of the triangle are

( ) (2 )2

d= x −x + y −y for d≥0

80 The midpoint formula results in an

ordered pair The x-coordinate of the midpoint is the average of the x- coordinates of the endpoints The y-

coordinate of the midpoint is the

average of the y-coordinates of the

endpoints

81 To find the x-intercept(s), substitute

0 for y and solve for x To find the intercept(s), substitute 0 for x and solve for y

y-82 The graph of the equation

represents the set of all solutions to the equation graphed in a

rectangular coordinate system

87 The viewing window is part of the

Cartesian plane shown in the display screen of a calculator The boundaries of the window are often denoted by [Xmin, Xmax, Xscl] by [Ymin, Ymax, Yscl]

88 780 42 5460

42 780 5460

780 546042130

1307

x y

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b

18 a ( ) ( )

( ) ( ) ( ) ( ) ( )

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2 6,

4 2, 2,1

7 5,

12 2, 6,1

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29 a The circle must touch the y-axis at

( )0,6 , at one side of a diameter

30 a The circle must touch the x-axis at

( )−2,0 , at one side of a diameter

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from the center Since the center

is in quadrant IV, the center must

32 a The circle must touch the x-axis

and the y-axis at a distance r from

the center Since the center is in quadrant II, the center must be ( )−3,3

11

11 11

x y

{ }

40 ( ) (2 )2

x+ + y− = − The sum of two squares cannot be negative, so there is no solution

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502

9

493

2 2

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2 2

1

3 1 94

59 A circle is the set of all points in a

plane that are equidistant from a fixed point called the center

60 The center and radius can easily be

identified from an equation of a circle written in standard form

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63 ( ) (2 )2

2 2 2

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2 2

3 +6 =3 5 Therefore, the distance between the origin and the point on the circle is

2 10−3

71 −15.1,15.1,1 by 10,10,1 − 

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7 Yes For a given time after tree is

planted, there cannot be two or more

That is, the height is unique at any given time

8 No There are numerous times during

the year when the temperature in Fort Collins, is 70 o

Therefore, given an input value of

70o, there is more than one output value (time)

9 a {(Tom Hanks, 5), (Jack Nicholson,

12), (Sean Penn, 5), (Dustin

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b {Tom Hanks, Jack Nicholson, Sean

Penn, Dustin Hoffman}

c {5, 12, 7}

d Yes

10 a {(Albany, 285), (Denver, 5883),

(Miami, 11), (San Francisco, 11)}

b {Albany, Denver, Miami, San

15 No vertical line intersects the graph

in more than one point This relation

is a function

17 There is at least one vertical line that

intersects the graph in more than one point

This relation is not a function

is a function

intersects the graph in more than

one point This relation is not a function

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is a function

intersects the graph in more than one point

This relation is not a function

23 This mapping defines the set of

ordered pairs:

( ) ( ) ( ) ( )

{ −8,3 ,−8,4 ,−8,5 ,−8,6} All four ordered pairs have the same

x value but different y values This

relation is not a function

ordered pairs: { ( ) ( ) ( )1,4 , 2,5 , 3,5}

No two ordered pairs have the same

relation is a function

27 ( ) (2 )2

x+ + y+ =

This equation represents the graph

of a circle with center (− −1, 5) and radius 5 This relation is not a function because it fails the vertical line test

28 ( ) (2 )2

x+ + y+ = This equation represents the graph

of a circle with center (− −3, 4) and radius 1 This relation is not a function because it fails the vertical line test

29 y= + x 3

No vertical line intersects the graph

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No vertical line intersects the graph in more than one point This relation is a function

b 2 2

Two or more ordered pairs have the same x value but different y values This

32 a y x

=

= ±

No vertical line intersects the graph in more than one point

This relation is a function

Two or more ordered pairs have

the same x value but different y

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g = Undefined

54 k( ) ( )−10 = −10 + = −1 9 Undefined

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