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Solution Manual for Intermediate Algebra for College Students, 7th Edition

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    S OLUTIONS M ANUAL D ANIEL S. M ILLER Niagara County Community College I NTERMEDIATE A LGEBRA FOR C OLLEGE S TUDENTS S EVENTH E DITION Robert Blitzer Miami Dade College

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    TABLE OF CONTENTS for INSTRUCTOR SOLUTIONS I NT ERMEDIATE A LGEBRA FOR C OLLEGE S TUDENTS 7 E Chapter 1: Algebra, Mathematical Models, and Problem Solving 1 Chapter 2: Functions and Linear Functions 67 Chapter 3: Systems of Linear Functions 131 Chapter 4: Inequalities and Problem Solving 251 Chapter 5: Polynomials, Polynomial Functions, and Factoring 331 Chapter 6: Rational Expressions, Functions, and Equations 423 Chapter 7: Radicals, Radical Functions, and Rational Exponents 587 Chapter 8: Quadratic Equations and Functions 677 Chapter 9: Exponential and Logarithmic Functions 839 Chapter 10: Conic Sections and Systems of Nonlinear Equations 943 Chapter 11: Sequences, Series, and the Binomial Theorem 1051

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    Chapter 1 Algebra, Mathematical Models, and Problem Solving 1 1.1 Check Points 1. a.  eight times a number five more 8 5 8 5 x x         b.  the quotient of a decreased by number and seven twice the number 2 2 7 7 x x x x        2. replace with 10 23 0.12 23 0.12(10) 23 1.2 21.8 x x          At age 10, the average neurotic level is 21.8. 3. replace with 13 2 2 2 8 6( 3) 8 6(13 3) 8 6(10) 8 6(100) 8 600 608 x x                 4. a. 2010 is 10 years after 2000. replace with 10 2 2 46 541 17,650 46(10) 541(10) 17,650 46(100) 541(10) 17,650 4600 5410 17,650 27,660 x D x x D               The formula indicates that the mean student-loan debt for college students who graduated in 2010 was $27,660. b. The model value, $27,660, is more than the actual data value, $26,682. Thus, the mathematical model overestimates by $978. 5. a. true; Because the number 13 is an element of the set of integers. b. true; Because 6 is not an element of {7, 8, 9, 10}, the statement is true. 6. a. 8  is less than 2;  true b. 7 is greater than 3;  true c. 1  is less than or equal to 4;  false d. 5 is greater than or equal to 5; true e. 2 is greater than or equal to 14;  true 7. a.   2 5 x x    b.   1 3.5 x x   c.   1 x x   1.1 Concept and Vocabulary Check 1. variable 2. expression 3. b th to the n th power; base; exponent 4. formula; modeling; models 5. natural 6. whole 7. integers 8. rational 9. irrational 10. rational; irrational 11. left 12. 2; 5; 2; 5 13. greater than 14. less than or equal to

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    Chapter 1 Algebra, Mathematical Models, and Problem Solving 2 1.1 Exercise Set 1. 5 x  2. 6 x  3. 4 x  4. 9 x  5. 4 x 6. 2 x 7. 2 10 x  8. 5 4 x  9. 1 6 2 x  10. 1 3 2 x  11. 4 2 x  12. 5 3 x  13. 3 5 x  14. 6 10 x  15. 7 5(10) 7 50 57     16.   8 6 5 8 30 38     17. 6(3) 8 18 8 10     18.   8 3 4 24 4 20     19.     2 1 1 1 1 3 3 9 9 3 1 1     20.     2 1 1 1 1 2 2 4 4 2 1 1     21. 2 7 6(7) 3 49 42 3 7 3 10         22.   2 8 7 8 4 64 56 4 8 4 12         23. 3 3 4 5(9 7) 4 5(2) 4 5(8) 4 40 44          24.       3 3 6 5 8 6 6 5 2 6 5 8 6 40 46          25. 2 8 3(8 2) 64 3(6) 64 18 46        26.     2 8 4 8 3 64 4 5 64 20 44        27. {1, 2, 3, 4} 28. {1, 2, 3} 29. {–7, –6, –5, –4} 30. {–6, –5, –4, –3} 31. {8, 9, 10, . . .} 32. {10, 11, 12, . . .} 33. {1, 3, 5, 7, 9} 34. {1, 3, 5, 7} 35. true; Seven is an integer. 36. true; Nine is an integer. 37. true; Seven is a rational number. 38. true; Nine is a rational number. 39. false; Seven is a rational number. 40. false; Nine is not an irrational number. 41. true; Three is not an irrational number. 42. true; Five is not an irrational number. 43. false; 1 2 is a rational number. 44. false; 1 4 is a rational number. 45. true; 2 is not a rational number. 46. true; π is not a rational number. 47. false; 2 is a real number.

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    Section 1.1 Algebraic Expressions, Real Numbers, and Interval Notation 3 48. false; π is a real number. 49. –6 is less than –2; true 50. –7 is less than –3; true 51. 5 is greater than –7; true 52. 3 is greater than –8; true 53. 0 is less than –4; false. 0 is greater than –4. 54. 0 is less than –5; false. 0 is greater than –5. 55. –4 is less than or equal to 1; true 56. –5 is less than or equal to 1; true 57. –2 is less than or equal to –6; false. –2 is greater than –6. 58. –3 is less than or equal to –7; false. –3 is greater than –7. 59. –2 is less than or equal to –2; true 60. –3 is less than or equal to –3; true 61. –2 is greater than or equal to –2; true 62. –3 is greater than or equal to –3; true 63. 2 is less than or equal to 1 2  ; false. 2 is greater than 1 2  . 64. 4 is less than or equal to 1 2  ; false. 4 is greater than 1 2  . 65.   1 6 x x   66.   2 4 x x    67.   5 2 x x    68.   4 3 x x    69.   3 1 x x    70.   2 5 x x    71.   2 x x  72.   3 x x  73.   3 x x   74.   5 x x   75.   3 x x  76.   2 x x  77.   5.5 x x  78.   3.5 x x  79. true 80. true 81. false;     3 1, 2,3, 4  . 82. false;     4 1, 2, 3, 4,5  .

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    Chapter 1 Algebra, Mathematical Models, and Problem Solving 4 83. true 84. true 85. false; The value of { x | x is an integer between 3  and 0} = { 2, 1}   , not { 3, 2, 1,0}    . 86. false; The value of { x | x is an integer between 4  and 0} = { 3, 2, 1}    , not { 4, 3, 2, 1, 0}     . 87. false; Twice the sum of a number and three is represented by   2 3 x  , not 2 3 x  . 88. false; Three times the sum of a number and five is represented by   3 5 x  , not 3 5 x  . 89. 4.6 0.02 4.6 0.02(20) 4.2 R x      The average resistance to happiness at age 20 is 4.2. 90. 4.6 0.02 4.6 0.02(30) 4.0 R x      The average resistance to happiness at age 30 is 4.0. 91. [4.6 0.02(30)] [4.6 0.02(50)] 4.0 3.6 0.4       The difference between the average resistance to happiness at age 30 and at age 50 is 0.4. 92. [4.6 0.02(20)] [4.6 0.02(70)] 4.2 3.2 1.0       The difference between the average resistance to happiness at age 20 and at age 70 is 0.4. 93.     2 2 32 8.7 0.3 32 8.7 4 0.3 4 32 34.8 4.8 62 S x x           According to the formula, 67% of American adults used smartphones to go online in 2013. The formula underestimated the actual value by 1%. 94.     2 2 32 8.7 0.3 32 8.7 3 0.3 3 32 26.1 2.7 55.4 S x x           According to the formula, 55.4% of American adults used smartphones to go online in 2012. The formula overestimated the actual value by 0.4%. 95. 5 (50 32) 9 C   5 (18) 10 9   10 ° C is equivalent to 50 ° F. 96. 5 5 5 ( 32) (86 32) (54) 30 9 9 9 C F       30 ° C is equivalent to 86 ° F. 97. 2 2 4 60 16 4 60(2) 16(2) 4 120 16(4) 4 120 64 124 64 60 h t t                Two seconds after it was kicked, the ball’s height was 60 feet. 98. 2 2 4 60 16 4 60(3) 16(3) 4 180 16(9) 4 180 144 184 144 40 h t t                Three seconds after it was kicked, the ball’s height was 40 feet. 99. – 116. Answers will vary. 117. does not make sense; Explanations will vary. Sample explanation: Many models work for a while and then no longer are valid beyond a certain point. 118. does not make sense; Explanations will vary. Sample explanation: Though this value is beyond the capabilities of a calculator, it still exists. This particular expression can be obtained via several software applications. 119. makes sense 120. does not make sense; Explanations will vary. Sample explanation: The model can be used to estimate the number in 2000 by letting 0. x 

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    Section 1.2 Operations with Real Numbers and Simplifying Algebraic Expression 5 121. false; Changes to make the statement true will vary. A sample change is: Every integer is a rational number. 122. false; Changes to make the statement true will vary. A sample change is: Some integers are not whole numbers. 123. true 124. true 125. Evaluate the two expressions.     2 4 20 2 24 48    2 4 20 8 20 28      Since the bird lover purchases 1 7 of the birds, the expression has to be a multiple of 7. Since 48 in not a multiple of 7 and 28 is a multiple of 7, we know that the correct expression is 2 4 20.   126.   2 3 3 5 45     127.     8 2 4 3 10     or   8 2 4 3 10     128. 26 is not a perfect square and 26 cannot be simplified. Consider the numbers closest to 26, both smaller and larger, which are perfect squares. The first perfect square smaller than 26 is 25. The first perfect square larger than 26 is 36. We know that the square root of 26 will lie between these numbers. We have 36 26 25.      If we simplify, we have 6 26 5.      Therefore, 26  lies between –6 and –5. 129. –5 and 5 are both a distance of five units from zero on a real number line. 130. 4 16 3(2) 16 3(16) 16 48 64 8 12 (10 6) 12 (4) 8 8           131. 2(3 5) 2(3(4) 5) 2(12 5) 2(17) 34 x        6 10 6(4) 10 24 10 34 x       1.2 Check Points 1. a. 6 6   because 6  is 6 units from 0. b. 4.5 4.5  because 4.5 is 4.5 units from 0. c. 0 0  because 0 is 0 units from 0. 2. a. 10 ( 18) 28      b. 0.2 0.9 0.7    c. 3 1 6 5 1 5 2 10 10 10        3. a. If 8, x   then ( 8) 8. x      b. If 1 3 , x  then 1 3 . x    4. a. 7 10 7 ( 10) 3       b. 4.3 ( 6.2) 4.3 6.2 10.5      c. 4 1 4 1 3 5 5 5 5 5               5. a. 2 ( 5) ( 5)( 5) 25      b. 2 5 (5 5) 25       c. 3 ( 4) ( 4)( 4)( 4) 64        d. 4 3 3 3 3 3 81 5 5 5 5 5 625                                      6. a. 32 8 4    b. 2 5 2 4 8 3 4 3 5 15                     7. 2 2 3 5 12 2( 4) 3 25 12 2(16) 3 25 6(16) 3 25 96 22 96 74                  

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    Chapter 1 Algebra, Mathematical Models, and Problem Solving 6 8. 3 4 3( 2) 2 (6 9) 4 3( 8) 2 ( 3) 4 24 2 3 20 5 4                 9. Commutative Property of Addition: 4 9 9 4 x x    Commutative Property of Multiplication: 4 9 4 9 x x     10. a. 6 (12 ) (6 12) 18 x x x        b. 7(4 ) ( 7 4) 28 x x x       11. 4(7 2) 28 8 x x      12. 2 2 2 2 2 2 3 14 11 (14 ) (3 11 ) (14 1) (3 11) 15 14 x x x x x x x x x x x x              13. 8(2 5) 4 16 40 4 16 4 40 12 40 x x x x x x x           14. 6 4[7 ( 2)] 6 4[7 2] 6 4[9 ] 6 36 4 42 4 x x x x x                1.2 Concept and Vocabulary Check 1. negative number 2. 0 3. positive number 4. positive number 5. positive number 6. negative number 7. positive number 8. divide 9. subtract 10. absolute value; 0; a 11. a ; a  12 . 0; inverse; 0; identity 13. b a  14. ( ) ab c 15. ab ac  16. simplified 1.2 Exercise Set 1. 7 7   2. 10 10   3. 4 4  4. 13 13  5. 7.6 7.6   6. 8.3 8.3   7. 2 2 π π  8. 3 3 π π  9. 2 2   10. 3 3   11. 2 2 5 5     12. 7 7 10 10    

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    Section 1.2 Operations with Real Numbers and Simplifying Algebraic Expression 7 13. 3 ( 8) 11      14. 5 ( 10) 15      15. 14 10 4     16. 15 6 9     17. 6.8 2.3 4.5     18. 7.9 2.4 5.5     19. 11 3 11 9 2 15 5 15 15 15                   20. 7 4 7 4 2 10 5 10 5 2 7 8 1 10 10 10                                   21. 2 3 2 3 9 4 9 4 8 27 35 36 36 36                         22. 3 4 3 4 5 7 5 7 21 20 41 35 35 35                         23. 3.7 ( 4.5) 8.2      24. 6.2 ( 5.9) 12.1      25. 0 ( 12.4) 12.4     26. 0 ( 15.3) 15.3     27. 12.4 ( 12.4) 0    28. 15.3 ( 15.3) 0    29. 11 11 x x     30. 13 13 x x     31. 5 5 x x     32. 9 9 x x     33. 0 0 x x    34. 2 2 x x     35.   3 15 3 15 12       36.   4 20 4 20 16       37. 8 ( 10) 8 10 18      38. 7 ( 13) 7 13 20      39. 20 ( 5) 20 5 15         40. 30 ( 10) 30 10 20         41. 1 1 1 1 1 2 1 4 2 4 2 4 4 4                      42. 1 2 1 2 1 2 2 10 5 10 5 10 5 2 1 4 3 10 10 10                                     43. 2.3 ( 7.8) 2.3 7.8 5.5        44. 4.3 ( 8.7) 4.3 8.7 4.4        45.   0 2 0 2 2      46.   0 3 0 3 3      47. 9( 10) 90    48. 8( 10) 80    49.     3 11 33    50.     7 11 77    51.   15 15 1 13 13   

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    Chapter 1 Algebra, Mathematical Models, and Problem Solving 8 52.   11 11 1 13 13    53. 2 0 0    54. 3 0 0    55.           4 2 1 8 1 8        56.           5 3 2 15 2 30        57. 2( 3)( 1)( 2)( 4) ( 6)( 1)( 2)( 4) (6)( 2)( 4) ( 12)( 4) 48                 58.                    3 2 1 5 3 6 1 5 3 6 5 3 30 3 90                 59.      2 10 10 10 100      60.      2 8 8 8 64      61.     2 10 10 10 100      62.     2 8 8 8 64      63.       3 2 2 2 2 8        64.       3 3 3 3 3 27        65.        4 1 1 1 1 1 1        66.        4 4 4 4 4 4 256        67. Since a product with an odd number of negative factors is negative,   33 1 1.    68. A product with an odd number of negative factors is negative.   35 1 1    69. 3 1 1 1 1 1 2 2 2 2 8                                 70. 3 1 1 1 1 1 4 4 4 4 64                                 71. 12 3 4    72. 30 6 5    73. 90 45 2    74. 55 11 5    75. 0 0 4.6   76. 0 0 5.3   77. 4.6 0  is undefined. 78. 5.3 0  is undefined. 79. 1 7 1 9 9 2 9 2 7 14                     80. 1 3 1 5 5 2 5 2 3 6                     81. 2 6 5 30 6 15 5 1 2 2                      82. 2 8 9 72 8 36 9 1 2 2                      83. 4( 5) 6( 3) 20 ( 18) 20 18 2             84. 8( 3) 5( 6) 24 ( 30) 24 30 6            85. 2 2 3( 2) 4( 3) 3(4) 4(9) 12 36 24          86. 2 2 5( 3) 2( 2) 5(9) 2(4) 45 8 37        

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    Section 1.2 Operations with Real Numbers and Simplifying Algebraic Expression 9 87. 2 2 8 16 2 4 3 64 16 4 4 3 64 4 4 3 64 16 3 48 3 45                    88. 2 2 10 100 5 2 3 100 100 25 2 3 100 4 2 3 100 8 3 92 3 89                    89.     2 2 2 2 2 2 5 2 3 5 2 9 9 ( 2) 3 ( 2) 10 9 9 2 1 11 1 121                   90.       2 2 2 10 2 3 4 5 3 4 5 12 17 36 12 3 2 12 6 6             91.         8 3 2(2 5) 4(8 6) 8 3 2( 3) 4(2) 8 3 6 8 8 3 2 8 6 14                    92.           8 3 2(5 7) 5(4 2) 8 3 2( 2) 5(2) 8 3 4 10 8 3 4 10 8 3 6 8 18 26                            93.     2 2 4 3 4 12 8 8 5 8 3 3 3             94.     6 4 5 3 24 15 9 9 9 10 1 1             95.       2 2 2 5 6 2 3 7 1 2 4 89 3 25 89 3 5 1 2 4 89 75 1 8 7 1 14 14 2                     96. 2 2 2 12 3 5 2 3 12 3 5 4 9 7 3 36 7 3 6 12 3 5 13 10 36 12 3 5(13) 4 5(13) 26 26 20(13) 260 10 26 26                             97. 15 3 ( 1) 12 2 3 15 4 12 2 3 15 2 12 2 3 15 2 6 3 15 2 18 13 18 31                           98.   17 5 2 12 2 3 17 7 12 2 3 17 7 12 2 3 17 7 6 3 17 7 18 10 18 28                           99.             2 2 2 2 20 1 10 5 1 2 20 1 10 6 2 20 1 100 36 2 20 1 64 2 20 1 8 2 20 1 16 37                            100.         2 2 2 24 3 5 2 1 3 24 3(3) 1 3 24 9 2 24 3 4 8 4 2                          101. Commutative Property of Addition 4 10 10 4 x x    Commutative Property of Multiplication 4 10 4 10 x x     102. Commutative Property of Addition 5 30 30 5 x x    Commutative Property of Multiplication 5 30 5 30 x x     103. Commutative Property of Addition 7 5 5 7 x x     Commutative Property of Multiplication 7 5 7 5 x x    

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    Chapter 1 Algebra, Mathematical Models, and Problem Solving 10 104. Commutative Property of Addition 3 7 7 3 x x     Commutative Property of Multiplication 3 7 3 7 x x     105. 4 (6 ) (4 6) 10 x x x        106. 12 (3 ) (12 3) 15 x x x        107. 7(3 ) ( 7 3) 21 x x x       108. 10(5 ) ( 10 5) 50 x x x       109. 1 1 ( 3 ) 3 3 3 y y y              110. 1 1 ( 4 ) 4 4 4 y y y              111. 3(2 5) 3 2 3 5 6 15 x x x        112. 5(4 7) 5 4 5 7 20 35 x x x        113.   7(2 3) 7 2 7 3 14 21 x x x           114.   9(3 2) 9 3 9 2 27 18 x x x           115.   (3 6) 1 3 1 6 3 6 x x x           116.     (6 3) 1 6 1 3 6 3 x x x          117.   7 5 7 5 12 x x x x     118.   8 10 8 10 18 x x x x     119.   2 2 2 2 6 6 1 5 x x x x     120.   2 2 2 2 9 9 1 8 x x x x     121.     2 2 2 2 2 2 6 10 4 2 6 4 10 2 6 4 10 2 10 12 x x x x x x x x x x x x              122.     2 2 2 2 9 5 3 4 9 3 5 4 12 9 x x x x x x x x          123.   8(3 5) 6 8 3 8 5 6 24 40 6 24 6 40 24 6 40 18 40 x x x x x x x x x x                   124.   7(4 5) 8 7 4 7 5 8 28 35 8 28 8 35 20 35 x x x x x x x x                125.       5(3 2) 7 2 5 3 5 2 1 7 1 2 15 10 7 2 15 7 10 2 15 7 12 8 12 y y y y y y y y y y                         126.         4(5 3) 6 3 4 5 4 (3) 1 6 1 3 20 12 6 3 20 6 15 14 15 y y y y y y y y                    127.     7 4 3 4 5 7 4 3 4 5 7 12 16 20 16 25 y y y y                  128.          6 5 8 2 4 6 5 8 2 4 6 5 12 2 6 5 12 5 2 6 60 10 10 54 y y y y y y                         129.     2 2 2 2 2 2 2 2 2 2 2 2 18 4 6 2 5 18 4 6 12 5 18 4 6 7 18 4 6 7 18 6 4 7 18 6 11 12 11 x x x x x x x x x x x x                                      

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    Section 1.2 Operations with Real Numbers and Simplifying Algebraic Expression 11 130.   2 2 2 2 2 2 14 5 7 2 4 14 5 7 14 4 14 5 7 10 x x x x x x                            2 2 2 2 2 2 14 5 7 10 14 7 5 10 14 7 15 7 15 x x x x x x              131.   4 4 4 x x x x        132.   8 8 2 8 x x x x x        133.   6 5 30 x x    134.   10 4 40 x x    135. 5 2 3 x x x   136.   6 2 6 2 8 x x x x x      137.   8 3 6 8 3 6 5 6 x x x x x        138.   8 3 6 8 3 18 3 10 x x x         139. 21 ( 29) 8     140. 4 ( 10) 6     141. 21 ( 29) 21 29 50      142. 4 ( 10) 4 10 14      143. 3 ( 10) 3 10 7        The approval rating of France exceeds the approval rating of China by 7. 144. 3 ( 29) 3 29 26        The approval rating of France exceeds the approval rating of Iran by 26. 145. 10 ( 3) 4 9 3 3 3         The average approval rating of China, France, and Israel is 3.  146. 29 ( 10) 21 18 3 3 6         The average approval rating of Iran, China, and the UK is 6.  147.   2 2 1.2 1.6( 40) 1.2 6 1.6(6 40) 116.8 D x x        According to the model, college students spent $116.8 billion in 2013. The model underestimates the actual value displayed in the graph by $0.2 billion. 148.   2 2 1.2 1.6( 40) 1.2 4 1.6(4 40) 89.6 D x x        According to the model, college students spent $89.6 billion in 2011. The model overestimates the actual value displayed in the graph by $2.6 billion. 149. a.   0.05 0.12 10,000 0.05 1200 0.12 1200 0.07 x x x x x        b.         0.05 6000 0.12 10,000 6000 0.05 6000 0.12 4000 300 480 780          1200 0.07 6000 1200 420 780     The total interest will be $780. 150. a. 0.06 0.5(50 ) 0.06 25 0.5 25 0.44 t t t t t        b. 0.06(20) 0.5(50 20) 0.06(20) 0.5(30) 1.2 15 16.2 25 0.44(20) 25 8.8 16.2            The total distance will be 16.2 miles.

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    Chapter 1 Algebra, Mathematical Models, and Problem Solving 12 151. – 167. Answers will vary. 168. makes sense 169. makes sense 170. does not make sense; Explanations will vary. Sample explanation: For terms to be considered like terms they must have the same variables and the same powers. 171. does not make sense; Explanations will vary. Sample explanation: When there is no number in front of a variable, the coefficient has a value of 1. 172. false; Changes to make the statement true will vary. A sample change is: 16 4 2 4 2 8      173. false; Changes to make the statement true will vary. A sample change is:     6 2 4 3 6 2 7 6 14 8         174. false; Changes to make the statement true will vary. A sample change is: 5 3( 4) 5 3 12 3 7 x x x        175. false; Changes to make the statement true will vary. A sample change is: 2 x x x     176. true 177. (8 2) 3 4 14     178. 1 2 5 10 9 45 2            179.     2 2 9 4 (1 6) (3 9) 9 4 7 ( 6) 12 12 5 5 6 6 5 5 2 1 3                9 3 36 12 5 5 2 27 36 12 5 3 63 5 4 63 9 7                 180. 10 4 x x  181.   4 4 4 10 2( 5) 10 2(7 5) 10 2(2) 10 2 16 10 32 42 x             182. true; 1 2 is not an irrational number. 183. x 2 4 y x   − 3 2 4 ( 3) 4 9 5 y        − 2 2 4 ( 2) 4 4 0 y       − 1 2 4 ( 1) 4 1 3 y       0 2 4 (0) 4 0 4 y      1 2 4 (1) 4 1 3 y      2 2 4 (2) 4 4 0 y      3 2 4 (3) 4 9 5 y       184. x 2 1 y x   − 3 2 1 ( 3) 1 9 8 y        − 2 2 1 ( 2) 1 4 3 y        − 1 2 1 ( 1) 1 1 0 y       0 2 1 (0) 1 0 1 y      1 2 1 (1) 1 1 0 y      2 2 1 (2) 1 4 3 y       3 2 1 (3) 1 9 8 y       185. x 1 y x   − 4 4 1 3 3 y       − 3 3 1 2 2 y       − 2 2 1 1 1 y       − 1 1 1 0 0 y      0 0 1 1 1 y     1 1 1 2 2 y     2 2 1 3 3 y    

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    Section 1.3 Graphing Equations 13 1.3 Check Points 1. 2. Make a table: 2 2 2 2 2 2 2 2 1 ( , ) 3 1 ( 3) 8 ( 3, 8) 2 1 ( 2) 3 ( 2, 3) 1 1 ( 1) 0 ( 1, 0) 0 1 (0) 1 (0,1) 1 1 (1) 0 (1, 0) 2 1 (2) 3 (2, 3) 3 1 (3) 8 (3, 8) x y x x y y y y y y y y = − − = − − = − − − − = − − = − − − − = − − = − = − = = − = = − = − − = − = − − 3. Make a table: 1 ( , ) 4 4 1 3 3 ( 4,3) 3 3 1 2 2 ( 3, 2) 2 2 1 1 1 ( 2,1) 1 1 1 0 0 ( 1,0) 0 0 1 1 1 (0,1) 1 1 1 2 2 (1, 2) 2 2 1 3 3 (2,3) x y x x y y y y y y y y                                              4. a. The drug concentration is increasing from 0 to 3 hours. b. The drug concentration is decreasing from 3 to 13 hours. c. The drug’s maximum concentration is 0.05 milligram per 100 milliliters, which occurs after 3 hours. d. None of the drug is left in the body. 5. The minimum x -value is –100, the maximum x - value is 100, and the distance between consecutive tick marks is 50. The minimum y -value is –100, the maximum y -value is 100, and the distance between consecutive tick marks is 10. 1.3 Concept and Vocabulary Check 1. x -axis 2 . y -axis 3 . origin 4. quadrants; four 5. x -coordinate; y -coordinate 6 . solution; satisfies

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