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  1. Preface
  2. 1 Prerequisites
    1. Introduction to Prerequisites
    2. 1.1 Real Numbers: Algebra Essentials
    3. 1.2 Exponents and Scientific Notation
    4. 1.3 Radicals and Rational Exponents
    5. 1.4 Polynomials
    6. 1.5 Factoring Polynomials
    7. 1.6 Rational Expressions
    8. Key Terms
    9. Key Equations
    10. Key Concepts
    11. Review Exercises
    12. Practice Test
  3. 2 Equations and Inequalities
    1. Introduction to Equations and Inequalities
    2. 2.1 The Rectangular Coordinate Systems and Graphs
    3. 2.2 Linear Equations in One Variable
    4. 2.3 Models and Applications
    5. 2.4 Complex Numbers
    6. 2.5 Quadratic Equations
    7. 2.6 Other Types of Equations
    8. 2.7 Linear Inequalities and Absolute Value Inequalities
    9. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Review Exercises
    13. Practice Test
  4. 3 Functions
    1. Introduction to Functions
    2. 3.1 Functions and Function Notation
    3. 3.2 Domain and Range
    4. 3.3 Rates of Change and Behavior of Graphs
    5. 3.4 Composition of Functions
    6. 3.5 Transformation of Functions
    7. 3.6 Absolute Value Functions
    8. 3.7 Inverse Functions
    9. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Review Exercises
    13. Practice Test
  5. 4 Linear Functions
    1. Introduction to Linear Functions
    2. 4.1 Linear Functions
    3. 4.2 Modeling with Linear Functions
    4. 4.3 Fitting Linear Models to Data
    5. Key Terms
    6. Key Concepts
    7. Review Exercises
    8. Practice Test
  6. 5 Polynomial and Rational Functions
    1. Introduction to Polynomial and Rational Functions
    2. 5.1 Quadratic Functions
    3. 5.2 Power Functions and Polynomial Functions
    4. 5.3 Graphs of Polynomial Functions
    5. 5.4 Dividing Polynomials
    6. 5.5 Zeros of Polynomial Functions
    7. 5.6 Rational Functions
    8. 5.7 Inverses and Radical Functions
    9. 5.8 Modeling Using Variation
    10. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  7. 6 Exponential and Logarithmic Functions
    1. Introduction to Exponential and Logarithmic Functions
    2. 6.1 Exponential Functions
    3. 6.2 Graphs of Exponential Functions
    4. 6.3 Logarithmic Functions
    5. 6.4 Graphs of Logarithmic Functions
    6. 6.5 Logarithmic Properties
    7. 6.6 Exponential and Logarithmic Equations
    8. 6.7 Exponential and Logarithmic Models
    9. 6.8 Fitting Exponential Models to Data
    10. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  8. 7 The Unit Circle: Sine and Cosine Functions
    1. Introduction to The Unit Circle: Sine and Cosine Functions
    2. 7.1 Angles
    3. 7.2 Right Triangle Trigonometry
    4. 7.3 Unit Circle
    5. 7.4 The Other Trigonometric Functions
    6. Key Terms
    7. Key Equations
    8. Key Concepts
    9. Review Exercises
    10. Practice Test
  9. 8 Periodic Functions
    1. Introduction to Periodic Functions
    2. 8.1 Graphs of the Sine and Cosine Functions
    3. 8.2 Graphs of the Other Trigonometric Functions
    4. 8.3 Inverse Trigonometric Functions
    5. Key Terms
    6. Key Equations
    7. Key Concepts
    8. Review Exercises
    9. Practice Test
  10. 9 Trigonometric Identities and Equations
    1. Introduction to Trigonometric Identities and Equations
    2. 9.1 Solving Trigonometric Equations with Identities
    3. 9.2 Sum and Difference Identities
    4. 9.3 Double-Angle, Half-Angle, and Reduction Formulas
    5. 9.4 Sum-to-Product and Product-to-Sum Formulas
    6. 9.5 Solving Trigonometric Equations
    7. Key Terms
    8. Key Equations
    9. Key Concepts
    10. Review Exercises
    11. Practice Test
  11. 10 Further Applications of Trigonometry
    1. Introduction to Further Applications of Trigonometry
    2. 10.1 Non-right Triangles: Law of Sines
    3. 10.2 Non-right Triangles: Law of Cosines
    4. 10.3 Polar Coordinates
    5. 10.4 Polar Coordinates: Graphs
    6. 10.5 Polar Form of Complex Numbers
    7. 10.6 Parametric Equations
    8. 10.7 Parametric Equations: Graphs
    9. 10.8 Vectors
    10. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  12. 11 Systems of Equations and Inequalities
    1. Introduction to Systems of Equations and Inequalities
    2. 11.1 Systems of Linear Equations: Two Variables
    3. 11.2 Systems of Linear Equations: Three Variables
    4. 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
    5. 11.4 Partial Fractions
    6. 11.5 Matrices and Matrix Operations
    7. 11.6 Solving Systems with Gaussian Elimination
    8. 11.7 Solving Systems with Inverses
    9. 11.8 Solving Systems with Cramer's Rule
    10. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  13. 12 Analytic Geometry
    1. Introduction to Analytic Geometry
    2. 12.1 The Ellipse
    3. 12.2 The Hyperbola
    4. 12.3 The Parabola
    5. 12.4 Rotation of Axes
    6. 12.5 Conic Sections in Polar Coordinates
    7. Key Terms
    8. Key Equations
    9. Key Concepts
    10. Review Exercises
    11. Practice Test
  14. 13 Sequences, Probability, and Counting Theory
    1. Introduction to Sequences, Probability and Counting Theory
    2. 13.1 Sequences and Their Notations
    3. 13.2 Arithmetic Sequences
    4. 13.3 Geometric Sequences
    5. 13.4 Series and Their Notations
    6. 13.5 Counting Principles
    7. 13.6 Binomial Theorem
    8. 13.7 Probability
    9. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Review Exercises
    13. Practice Test
  15. A | Proofs, Identities, and Toolkit Functions
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
  17. Index

Try It

2.1 The Rectangular Coordinate Systems and Graphs

1.
x x y= 1 2 x+2 y= 1 2 x+2 ( x,y ) ( x,y )
−2 −2 y= 1 2 ( −2 )+2=1 y= 1 2 ( −2 )+2=1 ( −2,1 ) ( −2,1 )
−1 −1 y= 1 2 ( −1 )+2= 3 2 y= 1 2 ( −1 )+2= 3 2 ( 1, 3 2 ) ( 1, 3 2 )
0 0 y= 1 2 ( 0 )+2=2 y= 1 2 ( 0 )+2=2 ( 0,2 ) ( 0,2 )
1 1 y= 1 2 ( 1 )+2= 5 2 y= 1 2 ( 1 )+2= 5 2 ( 1, 5 2 ) ( 1, 5 2 )
2 2 y= 1 2 ( 2 )+2=3 y= 1 2 ( 2 )+2=3 ( 2,3 ) ( 2,3 )
This is an image of a graph on an x, y coordinate plane. The x and y-axis range from negative 5 to 5.  A line passes through the points (-2, 1); (-1, 3/2); (0, 2); (1, 5/2); and (2, 3).
2.

x-intercept is ( 4,0 ); ( 4,0 ); y-intercept is ( 0,3 ). ( 0,3 ).

This is an image of a line graph on an x, y coordinate plane. The x and y axes range from negative 4 to 6.  The function y = -3x/4 + 3 is plotted.
3.

125 =5 5 125 =5 5

4.

( 5, 5 2 ) ( 5, 5 2 )

2.2 Linear Equations in One Variable

1.

x=−5 x=−5

2.

x=−3 x=−3

3.

x= 10 3 x= 10 3

4.

x=1 x=1

5.

x= 7 17 . x= 7 17 . Excluded values are x= 1 2 x= 1 2 and x= 1 3 . x= 1 3 .

6.

x= 1 3 x= 1 3

7.

m= 2 3 m= 2 3

8.

y=4x−3 y=4x−3

9.

x+3y=2 x+3y=2

10.

Horizontal line: y=2 y=2

11.

Parallel lines: equations are written in slope-intercept form.

Coordinate plane with the x-axis ranging from negative 5 to 5 and the y-axis ranging from negative 1 to 6.  Two functions are graphed on the same plot: y = x/2 plus 5 and y = x/2 plus 2.  The lines do not cross.
12.

y=5x+3 y=5x+3

2.3 Models and Applications

1.

11 and 25

2.

C=2.5x+3,650 C=2.5x+3,650

3.

45 mi/h

4.

L=37 L=37 cm, W=18 W=18 cm

5.

250 ft2

2.4 Complex Numbers

1.

−24 =0+2i 6 −24 =0+2i 6

2.
Coordinate plane with the x and y axes ranging from negative 5 to 5.  The point -4  i is plotted.
3.

(3−4i)(2+5i)=1−9i (3−4i)(2+5i)=1−9i

4.

5 2 i 5 2 i

5.

18+i 18+i

6.

−3−4i −3−4i

7.

−1 −1

2.5 Quadratic Equations

1.

( x6 )( x+1 )=0;x=6, x=1 ( x6 )( x+1 )=0;x=6, x=1

2.

( x−7 )( x+3 )=0, ( x−7 )( x+3 )=0, x=7, x=7, x=−3. x=−3.

3.

( x+5 )( x−5 )=0, ( x+5 )( x−5 )=0, x=−5, x=−5, x=5. x=5.

4.

( 3x+2 )( 4x+1 )=0, ( 3x+2 )( 4x+1 )=0, x= 2 3 , x= 2 3 , x= 1 4 x= 1 4

5.

x=0,x=−10,x=−1 x=0,x=−10,x=−1

6.

x=4± 5 x=4± 5

7.

x=3± 22 x=3± 22

8.

x= 2 3 , x= 2 3 , x= 1 3 x= 1 3

9.

5 5 units

2.6 Other Types of Equations

1.

1 4 1 4

2.

25 25

3.

{ −1 } { −1 }

4.

0, 0, 1 2 , 1 2 , 1 2 1 2

5.

1; 1; extraneous solution 2 9 2 9

6.

−2; −2; extraneous solution −1 −1

7.

−1, −1, 3 2 3 2

8.

−3,3,i,i −3,3,i,i

9.

2,12 2,12

10.

−1, −1, 0 0 is not a solution.

2.7 Linear Inequalities and Absolute Value Inequalities

1.

[ −3,5 ] [ −3,5 ]

2.

( ,−2 )[ 3, ) ( ,−2 )[ 3, )

3.

x<1 x<1

4.

x−5 x−5

5.

( 2, ) ( 2, )

6.

[ 3 14 , ) [ 3 14 , )

7.

6<x9or( 6,9 ] 6<x9or( 6,9 ]

8.

( 1 8 , 1 2 ) ( 1 8 , 1 2 )

9.

| x−2 |3 | x−2 |3

10.

k1 k1 or k7; k7; in interval notation, this would be (,1][7,). (,1][7,).

A coordinate plane with the x-axis ranging from -1 to 9 and the y-axis ranging from -3 to 8.  The function y = -2|k  4| + 6 is graphed and everything above the function is shaded in.

2.1 Section Exercises

1.

Answers may vary. Yes. It is possible for a point to be on the x-axis or on the y-axis and therefore is considered to NOT be in one of the quadrants.

3.

The y-intercept is the point where the graph crosses the y-axis.

5.

The x-intercept is ( 2,0 ) ( 2,0 ) and the y-intercept is ( 0,6 ). ( 0,6 ).

7.

The x-intercept is ( 2,0 ) ( 2,0 ) and the y-intercept is ( 0,−3 ). ( 0,−3 ).

9.

The x-intercept is ( 3,0 ) ( 3,0 ) and the y-intercept is ( 0, 9 8 ). ( 0, 9 8 ).

11.

y=42x y=42x

13.

y= 52x 3 y= 52x 3

15.

y=2x 4 5 y=2x 4 5

17.

d= 74 d= 74

19.

d= 36 =6 d= 36 =6

21.

d62.97 d62.97

23.

( 3, 3 2 ) ( 3, 3 2 )

25.

( 2,−1 ) ( 2,−1 )

27.

( 0,0 ) ( 0,0 )

29.

y=0 y=0

31.


This is an image of an x, y coordinate plane with the x and y axes ranging from negative 5 to 5. The points (0,4); (-1,2) and (2,1) are plotted and labeled.

not collinear

33.

A: ( −3,2 ),B: ( 1,3 ),C: ( 4,0 ) A: ( −3,2 ),B: ( 1,3 ),C: ( 4,0 )

35.

x x y y
−3 −3 1
0 2
3 3
6 4
This is an image of an x, y coordinate plane with the x and y axes ranging from negative 10 to 10.  The points (-3, 1); (0, 2); (3, 3) and (6, 4) are plotted and labeled.  A line runs through all these points.
37.
x y
–3 0
0 1.5
3 3
This is an image of an x, y coordinate plane with the x and y axes ranging from negative 10 to 10.  The points (-3, 0); (0, 1.5) and (3, 3) are plotted and labeled.  A line runs through all of these points.
39.
This is an image of an x, y coordinate plane with the x and y axes ranging from negative 10 to 10.  The points (8, 0) and (0, -4) are plotted and labeled.  A line runs through both of these points.
41.
This is an image of an x, y coordinate plane with the x and y axes ranging from negative 10 to 10.  The points (0, 2) and (3, 0) are plotted and labeled.  A line runs through both of these points.
43.

d=8.246 d=8.246

45.

d=5 d=5

47.

( −3,4 ) ( −3,4 )

49.

x=0         y=−2 x=0         y=−2

51.

x=0.75     y=0 x=0.75     y=0

53.

x=1.667     y=0 x=1.667     y=0

55.

15−11.= 3.8 15−11.= 3.8 mi shorter

57.

6.042 6.042

59.

Midpoint of each diagonal is the same point ( 2,2 ). ( 2,2 ). Note this is a characteristic of rectangles, but not other quadrilaterals.

61.

37 37 mi

63.

54 ft

2.2 Section Exercises

1.

It means they have the same slope.

3.

The exponent of the x x variable is 1. It is called a first-degree equation.

5.

If we insert either value into the equation, they make an expression in the equation undefined (zero in the denominator).

7.

x=2 x=2

9.

x= 2 7 x= 2 7

11.

x=6 x=6

13.

x=3 x=3

15.

x=−14 x=−14

17.

x−4; x−4; x=−3 x=−3

19.

x1; x1; when we solve this we get x=1, x=1, which is excluded, therefore NO solution

21.

x0; x0; x= 5 2 x= 5 2

23.

y= 4 5 x+ 14 5 y= 4 5 x+ 14 5

25.

y= 3 4 x+2 y= 3 4 x+2

27.

y= 1 2 x+ 5 2 y= 1 2 x+ 5 2

29.

y=−3x5 y=−3x5

31.

y=7 y=7

33.

y=−4 y=−4

35.

8x+5y=7 8x+5y=7

37.


Coordinate plane with the x and y axes ranging from negative 10 to 10.  The functions 3 times x minus 2 times y = 5 and 6 times y minus 9 times x = 6 are graphed on the same plot.  The lines do not cross.

Parallel

39.


Coordinate plane with the x and y axes ranging from negative 10 to 10.  The function y = negative 3 and the line x = 4 are graphed on the same plot.  These lines cross at a 90 degree angle.

Perpendicular

41.

m= 9 7 m= 9 7

43.

m= 3 2 m= 3 2

45.

m 1 = 1 3 , m 2 =3;Perpendicular. m 1 = 1 3 , m 2 =3;Perpendicular.

47.

y=0.245x45.662. y=0.245x45.662.Answers may vary. y min =−50,  y max =−40 y min =−50,  y max =−40

49.

y=2.333x+6.667. y=2.333x+6.667. Answers may vary. y min =−10,  y max =10 y min =−10,  y max =10

51.

y= A B x+ C B y= A B x+ C B

53.

The slope for (−1,1) to (0,4) is 3. The slope for (−1,1) to (2,0) is  1 3 . The slope for (2,0) to (3,3) is 3. The slope for (0,4) to (3,3) is  1 3 . The slope for (−1,1) to (0,4) is 3. The slope for (−1,1) to (2,0) is  1 3 . The slope for (2,0) to (3,3) is 3. The slope for (0,4) to (3,3) is  1 3 .

Yes they are perpendicular.

55.

30 ft

57.

$57.50

59.

220 mi

2.3 Section Exercises

1.

Answers may vary. Possible answers: We should define in words what our variable is representing. We should declare the variable. A heading.

3.

2,000x 2,000x

5.

v+10 v+10

7.

Ann: 23; 23; Beth: 46 46

9.

20+0.05m 20+0.05m

11.

300 min

13.

90+40P 90+40P

15.

6 devices

17.

50,000x 50,000x

19.

4 h

21.

She traveled for 2 h at 20 mi/h, or 40 miles.

23.

$5,000 at 8% and $15,000 at 12%

25.

B=100+.05x B=100+.05x

27.

Plan A

29.

R=9 R=9

31.

r= 4 5 r= 4 5 or 0.8

33.

W= P2L 2 = 582(15) 2 =14 W= P2L 2 = 582(15) 2 =14

35.

f= pq p+q = 8(13) 8+13 = 104 21 f= pq p+q = 8(13) 8+13 = 104 21

37.

m= 5 4 m= 5 4

39.

h= 2A b 1 + b 2 h= 2A b 1 + b 2

41.

length = 360 ft; width = 160 ft

43.

405 mi

45.

A=88 in . 2 A=88 in . 2

47.

28.7

49.

h= V π r 2 h= V π r 2

51.

r= V πh r= V πh

53.

C=12π C=12π

2.4 Section Exercises

1.

Add the real parts together and the imaginary parts together.

3.

Possible answer: i i times i i equals -1, which is not imaginary.

5.

−8+2i −8+2i

7.

14+7i 14+7i

9.

23 29 + 15 29 i 23 29 + 15 29 i

11.


Coordinate plane with the x and y axes ranging from 5 to 5.  The point 1  2i is plotted
13.


Coordinate plane with the x and y axes ranging from -5 to 5.  The point i is plotted.
15.

8i 8i

17.

−11+4i −11+4i

19.

2−5i 2−5i

21.

6+15i 6+15i

23.

−16+32i −16+32i

25.

−4−7i −4−7i

27.

25

29.

2 2 3 i 2 2 3 i

31.

46i 46i

33.

2 5 + 11 5 i 2 5 + 11 5 i

35.

15i 15i

37.

1+i 3 1+i 3

39.

1 1

41.

−1 −1

43.

128i

45.

( 3 2 + 1 2 i ) 6 =−1 ( 3 2 + 1 2 i ) 6 =−1

47.

3i 3i

49.

0

51.

5−5i 5−5i

53.

−2i −2i

55.

9 2 9 2 i 9 2 9 2 i

2.5 Section Exercises

1.

It is a second-degree equation (the highest variable exponent is 2).

3.

We want to take advantage of the zero property of multiplication in the fact that if ab=0 ab=0 then it must follow that each factor separately offers a solution to the product being zero: a=0 or b=0. a=0 or b=0.

5.

One, when no linear term is present (no x term), such as x 2 =16. x 2 =16. Two, when the equation is already in the form (ax+b) 2 =d. (ax+b) 2 =d.

7.

x=6, x=6, x=3 x=3

9.

x= 5 2 , x= 5 2 , x= 1 3 x= 1 3

11.

x=5, x=5, x=−5 x=−5

13.

x= 3 2 , x= 3 2 , x= 3 2 x= 3 2

15.

x=−2,3 x=−2,3

17.

x=0, x=0, x= 3 7 x= 3 7

19.

x=−6, x=−6, x=6 x=6

21.

x=6, x=6, x=−4 x=−4

23.

x=1, x=1, x=−2 x=−2

25.

x=−2, x=−2, x=11 x=11

27.

x=3± 22 x=3± 22

29.

z= 2 3 , z= 2 3 , z= 1 2 z= 1 2

31.

x= 3± 17 4 x= 3± 17 4

33.

Not real

35.

One rational

37.

Two real; rational

39.

x= 1± 17 2 x= 1± 17 2

41.

x= 5± 13 6 x= 5± 13 6

43.

x= 1± 17 8 x= 1± 17 8

45.

x0.131 x0.131and x2.535 x2.535

47.

x6.7 x6.7and x1.7 x1.7

49.

a x 2 +bx+c = 0 x 2 + b a x = c a x 2 + b a x+ b 2 4 a 2 = c a + b 4 a 2 ( x+ b 2a ) 2 = b 2 4ac 4 a 2 x+ b 2a = ± b 2 4ac 4 a 2 x = b± b 2 4ac 2a a x 2 +bx+c = 0 x 2 + b a x = c a x 2 + b a x+ b 2 4 a 2 = c a + b 4 a 2 ( x+ b 2a ) 2 = b 2 4ac 4 a 2 x+ b 2a = ± b 2 4ac 4 a 2 x = b± b 2 4ac 2a

51.

x(x+10)=119; x(x+10)=119; 7 ft. and 17 ft.

53.

maximum at x=70 x=70

55.

The quadratic equation would be (100x−0.5 x 2 )(60x+300)=300. (100x−0.5 x 2 )(60x+300)=300. The two values of x x are 20 and 60.

57.

3 feet

2.6 Section Exercises

1.

This is not a solution to the radical equation, it is a value obtained from squaring both sides and thus changing the signs of an equation which has caused it not to be a solution in the original equation.

3.

He or she is probably trying to enter negative 9, but taking the square root of −9 −9 is not a real number. The negative sign is in front of this, so your friend should be taking the square root of 9, cubing it, and then putting the negative sign in front, resulting in −27. −27.

5.

A rational exponent is a fraction: the denominator of the fraction is the root or index number and the numerator is the power to which it is raised.

7.

x=81 x=81

9.

x=17 x=17

11.

x=8,  x=27 x=8,  x=27

13.

x=−2,1,−1 x=−2,1,−1

15.

y=0,   3 2 ,   3 2 y=0,   3 2 ,   3 2

17.

m=1,−1 m=1,−1

19.

x= 2 5 , ±3 i x= 2 5 , ±3 i

21.

x=32 x=32

23.

t= 44 3 t= 44 3

25.

x=3 x=3

27.

x=−2 x=−2

29.

x=4, −4 3 x=4, −4 3

31.

x= 5 4 , 7 4 x= 5 4 , 7 4

33.

x=3,−2 x=3,−2

35.

x=−5 x=−5

37.

x=1,−1,3,-3 x=1,−1,3,-3

39.

x=2,−2 x=2,−2

41.

x=1,5 x=1,5

43.

All real numbers

45.

x=4,6,−6,−8 x=4,6,−6,−8

47.

10 in.

49.

90 kg

2.7 Section Exercises

1.

When we divide both sides by a negative it changes the sign of both sides so the sense of the inequality sign changes.

3.

( , ) ( , )

5.

We start by finding the x-intercept, or where the function = 0. Once we have that point, which is (3,0), (3,0), we graph to the right the straight line graph y=x−3, y=x−3, and then when we draw it to the left we plot positive y values, taking the absolute value of them.

7.

( , 3 4 ] ( , 3 4 ]

9.

[ 13 2 , ) [ 13 2 , )

11.

( ,3 ) ( ,3 )

13.

( , 37 3 ] ( , 37 3 ]

15.

All real numbers ( , ) ( , )

17.

( , 10 3 )( 4, ) ( , 10 3 )( 4, )

19.

( ,−4 ][ 8,+ ) ( ,−4 ][ 8,+ )

21.

No solution

23.

( −5,11 ) ( −5,11 )

25.

[ 6,12 ] [ 6,12 ]

27.

[ −10,12 ] [ −10,12 ]

29.

x>6 and x>2 Take the intersection of two sets. x>2,(2,+) x>6 and x>2 Take the intersection of two sets. x>2,(2,+)

31.

x<3orx1 Take the union of the two sets. (,3) [1,) x<3orx1 Take the union of the two sets. (,3) [1,)

33.

( ,−1 )( 3, ) ( ,−1 )( 3, )


A coordinate plane where the x and y axes both range from -10 to 10.  The function |x  1| is graphed and labeled along with the line y = 2.  Along the x-axis there is an open circle at the point -1 with an arrow extending leftward from it.  Also along the x-axis is an open circle at the point 3 with an arrow extending rightward from it.
35.

[ −11,−3 ] [ −11,−3 ]


A coordinate plane with the x-axis ranging from -14 to 10 and the y-axis ranging from -1 to 10.  The function y = |x + 7| and the line y = 4 are graphed.  On the x-axis theres a dot on the points -11 and -3 with a line connecting them.
37.

It is never less than zero. No solution.


A coordinate plane with the x and y axes ranging from -10 to 10.  The function y = |x -2| and the line y = 0 are graphed.
39.

Where the blue line is above the orange line; point of intersection is x=3. x=3.

( ,−3 ) ( ,−3 )


A coordinate plane with the x and y axes ranging from -10 to 10.  The lines y = x - 2 and y = 2x + 1 are graphed on the same axes.
41.

Where the blue line is above the orange line; always. All real numbers.

(,) (,)


A coordinate plane with the x and y axes ranging from -10 to 10.  The lines y = x/2 +1 and y = x/2  5 are both graphed on the same axes.
43.

( −1,3 ) ( −1,3 )

45.

( ,4 ) ( ,4 )

47.

{ x| x<6 } { x| x<6 }

49.

{ x| −3x<5 } { x| −3x<5 }

51.

( −2,1 ] ( −2,1 ]

53.

( ,4 ] ( ,4 ]

55.

Where the blue is below the orange; always. All real numbers. (,+). (,+).


A coordinate plane with the x and y axes ranging from -10 to 10.  The function y = -0.5|x + 2| and the line y = 4 are graphed on the same axes.  A line runs along the entire x-axis.
57.

Where the blue is below the orange; ( 1,7 ). ( 1,7 ).


A coordinate plane with the x and y axes ranging from -10 to 10.  The function y = |x  4| and the line y = 3 are graphed on the same axes.  Along the x-axis the points 1 and 7 have an open circle around them and a line connects the two.
59.

x=2, 4 5 x=2, 4 5

61.

( −7,5 ] ( −7,5 ]

63.

80T120 1,60020T2,400 80T120 1,60020T2,400

[ 1,600, 2,400 ] [ 1,600, 2,400 ]

Review Exercises

1.

x-intercept: ( 3,0 ); ( 3,0 ); y-intercept: ( 0,−4 ) ( 0,−4 )

3.

y= 5 3 x+4 y= 5 3 x+4

5.

72 =6 2 72 =6 2

7.

620.097 620.097

9.

midpoint is ( 2, 23 2 ) ( 2, 23 2 )

11.

x y
0 −2
3 2
6 6


A coordinate plane with the x and y axes ranging from -10 to 10.  The points (0,-2); (3,2) and (6,6) are plotted and a line runs through all these points.
13.

x=4 x=4

15.

x= 12 7 x= 12 7

17.

No solution

19.

y= 1 6 x+ 4 3 y= 1 6 x+ 4 3

21.

y= 2 3 x+6 y= 2 3 x+6

23.

females 17, males 56

25.

84 mi

27.

x= 3 4 ± i 47 4 x= 3 4 ± i 47 4

29.

horizontal component −2; −2; vertical component −1 −1

31.

7+11i 7+11i

33.

16i 16i

35.

−1630i −1630i

37.

−4i 10 −4i 10

39.

x=73i x=73i

41.

x=−1,−5 x=−1,−5

43.

x=0, 9 7 x=0, 9 7

45.

x=10,−2 x=10,−2

47.

x= 1± 5 4 x= 1± 5 4

49.

x= 2 5 , 1 3 x= 2 5 , 1 3

51.

x=5±2 7 x=5±2 7

53.

x=0,256 x=0,256

55.

x=0,± 2 x=0,± 2

57.

x=−2 x=−2

59.

x= 11 2 , −17 2 x= 11 2 , −17 2

61.

( ,4 ) ( ,4 )

63.

[ 10 3 ,2 ] [ 10 3 ,2 ]

65.

No solution

67.

( 4 3 , 1 5 ) ( 4 3 , 1 5 )

69.

Where the blue is below the orange line; point of intersection is x=3.5. x=3.5.

( 3.5, ) ( 3.5, )


A coordinate plane with the x and y axes ranging from -10 to 10.  The lines y = x + 3 and y = 3x -4 graphed on the same axes.

Practice Test

1.

y= 3 2 x+2 y= 3 2 x+2

x y
0 2
2 5
4 8


A coordinate plane with the x and y axes ranging from -10 to 10.  The line going through the points (0,2); (2,5); and (4,8) is graphed.
3.

( 0,−3 ) ( 0,−3 ) ( 4,0 ) ( 4,0 )


A coordinate plane with the x and y axes ranging from -10 to 10.  The points (4,0) and (0,-3) are plotted with a line running through them.
5.

( ,9 ] ( ,9 ]

7.

x=−15 x=−15

9.

x−4,2; x−4,2; x= 5 2 ,1 x= 5 2 ,1

11.

x= 3± 3 2 x= 3± 3 2

13.

( −4,1 ) ( −4,1 )

15.

y= −5 9 x 2 9 y= −5 9 x 2 9

17.

y= 5 2 x4 y= 5 2 x4

19.

14i 14i

21.

5 13 14 13 i 5 13 14 13 i

23.

x=2, 4 3 x=2, 4 3

25.

x= 1 2 ± 2 2 x= 1 2 ± 2 2

27.

4 4

29.

x= 1 2 ,2,−2 x= 1 2 ,2,−2

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