Download Write a verbal expression for each algebraic

algebraic expression x + 9.
ANSWER: x +9
Study Guide and Review -Chapter 1
Write a verbal expression for each algebraic
expression.
8. h – 7
SOLUTION: The expression shows h minus seven. So, the verbal
expression the difference between h and 7 can be
used to describe the algebraic expression h – 7.
ANSWER: the difference between h and 7
9. 3x
12. two thirds of a number d to the third power
SOLUTION: The words two-thirds of suggest multiplication. So,
the verbal expression two-thirds of a number d to
the third power can be written as the algebraic
expression
.
ANSWER: 2
13. 5 less than four times a number
SOLUTION: The expression shows the product of the factors 3
2
2
and x . The factor x represents a number raised to
the second power or squared. So, the verbal
expression, the product of 3 and x squared can be
used to describe the algebraic expression 3x .
SOLUTION: Let x represent a number. The words less than
suggest subtraction, and the word times suggests
multiplication So, the verbal expression 5 less than
four times a number can be written as the algebraic
expression 4x – 5.
ANSWER: the product of 3 and x squared
ANSWER: 4x – 5
2
Evaluate each expression.
3
10. 5 + 6m
5
14. 2
SOLUTION: 3
The expression shows the sum of 5 and 6m . The
3
term 6m represents the product of the factors 6 and
3
SOLUTION: 3
m . The factor m represents a number raised to the
third power or cubed. So, the verbal expression five
more than the product of six and m cubed can be
3
used to describe the algebraic expression 5 + 6m .
ANSWER: five more than the product of six and m cubed
ANSWER: 32
3
15. 6
SOLUTION: Write an algebraic expression for each verbal
expression.
11. a number increased by 9
SOLUTION: Let x represent a number. The word increased
suggests addition. So, the verbal expression a
number increased by 9 can be written as the
algebraic expression x + 9.
ANSWER: 216
4
16. 4
SOLUTION: ANSWER: x +9
12. two thirds of a number d to the third power
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SOLUTION: The words two-thirds of suggest multiplication. So,
ANSWER: 256
Page 1
17. BOWLING Fantastic Pins Bowling Alley charges
$2.50 for shoe rental plus $3.25 for each game.
ANSWER: Study
Guide and Review -Chapter 1
216
4
ANSWER: 18
20. 7 + 2(9 – 3)
16. 4
SOLUTION: SOLUTION: ANSWER: 256
17. BOWLING Fantastic Pins Bowling Alley charges
$2.50 for shoe rental plus $3.25 for each game.
Write an expression representing the cost to rent
shoes and bowl g games.
SOLUTION: Let g represent the number of games. To find the
cost of g games, multiply the cost of one game,
$3.25, by g. To find the total cost, add the result to
the cost of shoe rental. So, the expression 2.50 +
3.25g represents the cost to rent shoes and bowl g
games.
ANSWER: 19
21. 8 ∙ 4 – 6 ∙ 5
SOLUTION: ANSWER: 2
5
22. [(2 – 5) ÷ 9]11
SOLUTION: ANSWER: 2.50 + 3.25g
Evaluate each expression.
18. 24 – 4 ∙ 5
SOLUTION: ANSWER: 33
ANSWER: 4
2
23. SOLUTION: 19. 15 + 3 – 6
SOLUTION: ANSWER: 18
20. 7 + 2(9 – 3)
SOLUTION: ANSWER: 3
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ANSWER: 19
Evaluate each expression if a = 4, b = 3, and c =
9.
Page 2
24. c + 3a
SOLUTION: ANSWER: Study
Guide and Review -Chapter 1
3
Evaluate each expression if a = 4, b = 3, and c =
9.
24. c + 3a
SOLUTION: Replace c with 9 and a with 4.
ANSWER: 10
27. ICE CREAM The cost of a one-scoop sundae is
$2.75, and the cost of a two-scoop sundae is $4.25.
Write and evaluate an expression to find the total
cost of 3 one-scoop sundaes and 2 two-scoop
sundaes.
SOLUTION: To find the cost of 3 one-scoop sundaes and 2 twoscoop sundaes, multiply the cost of a one-scoop
sundae by 3 and add that to the product of 2 and the
cost of a two-scoop sundae. So, the expression 2.75
(3) + 4.25(2) can be used to find the total cost of 3
one-scoop sundaes and 2 two-scoop sundaes.
ANSWER: 21
2
25. 5b ÷ c
SOLUTION: Replace b with 3 and c with 9.
The total cost of 3 one-scoop sundaes and 2 twoscoop sundaes is $16.75.
ANSWER: 2.75(3) + 4.25(2); $16.75
Evaluate each expression using properties of
numbers. Name the property used in each step.
28. 18 ∙ 3(1 ÷ 3)
SOLUTION: 18 ∙ 3(1 ÷ 3)
ANSWER: 5
Substitution
= 18 ∙ (3)
2
26. (a + 2bc) ÷ 7
Multiplicative Inverse
Multiplicative Identity
= 18 ∙ 1
= 18
SOLUTION: Replace a with 4, b with 3 and c with 9.
ANSWER: 18 ∙ 3(1 ÷ 3)
Substitution
= 18 ∙ (3)
Multiplicative
Inverse
Multiplicative
Identity
= 18 ∙ 1
= 18
29. ANSWER: 10
SOLUTION: 27. ICE CREAM The cost of a one-scoop sundae is
$2.75,
and -the
cost by
of Cognero
a two-scoop sundae is $4.25.
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Write and evaluate an expression to find the total
cost of 3 one-scoop sundaes and 2 two-scoop
sundaes.
Substitution
Substitution
Page 3
= 18 ∙ 1
29. (16 – 4 ) + 9
= 16 – 16 + 9
=0 +9
=9
Inverse
= 18
Multiplicative
Identity
Study
Guide and Review -Chapter 1
Substitution
Additive Inverse
Additive Identity
31. SOLUTION: SOLUTION: Substitution
Substitution
Substitution
Multiplicative Inverse
Substitution
Multiplicative
Inverse
Multiplicative
Identity
Substitution
ANSWER: Substitution
ANSWER: Substitution
Multiplicative Inverse
Substitution
2
30. (16 – 4 ) + 9
Substitution
Multiplicative Inverse
Multiplicative Identity
Substitution
SOLUTION: 2
(16 – 4 ) + 9
= 16 – 16 + 9
=0 +9
=9
Substitution
Additive Inverse
Additive Identity
32. 18 + 41 + 32 + 9
SOLUTION: 18 + 41 + 32 + 9
= 18 + 32 + 41 + 9
= (18 + 32) + (41 + 9)
= 50 + 50
= 100
ANSWER: 2
(16 – 4 ) + 9
= 16 – 16 + 9
=0 +9
=9
Substitution
Additive Inverse
Additive Identity
Commutative (+)
Associative (+)
Substitution
Substitution
31. ANSWER: 18 + 41 + 32 + 9
= 18 + 32 + 41 + 9
= (18 + 32) + (41 + 9)
= 50 + 50
= 100
SOLUTION: Commutative (+)
Associative (+)
Substitution
Substitution
Substitution
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33. Substitution
Multiplicative
Inverse
Multiplicative
Identity
Substitution
SOLUTION: Page 4
Commutative (+)
Commutative (+)
= 18 + 32 + 41 + 9
Associative (+)
= (18 + 32) + (41 + 9)
Substitution
= 50 + 50
100 and Review -Chapter
Substitution
Study=Guide
1
= 8 ∙ 5 ∙ 0.5
= (8 ∙ 5) ∙ 0.5
= 40 ∙ 0.5
= 20
Commutative (×)
Associative (×)
Substitution
Substitution
33. 35. 5.3 + 2.8 + 3.7 + 6.2
SOLUTION: SOLUTION: Commutative (+)
Associative (+)
Substitution
Substitution
Commutative (+)
Associative (+)
Substitution
Substitution
ANSWER: ANSWER: Commutative (+)
Associative (+)
Substitution
Substitution
Commutative (+)
Associative (+)
Substitution
Substitution
34. 8 ∙ 0.5 ∙ 5
SOLUTION: 8 ∙ 0.5 ∙ 5
= 8 ∙ 5 ∙ 0.5
= (8 ∙ 5) ∙ 0.5
= 40 ∙ 0.5
= 20
Commutative (×)
Associative (×)
Substitution
Substitution
ANSWER: 8 ∙ 0.5 ∙ 5
= 8 ∙ 5 ∙ 0.5
= (8 ∙ 5) ∙ 0.5
= 40 ∙ 0.5
= 20
36. SCHOOL SUPPLIES Monica needs to purchase a
binder, a textbook, a calculator, and a workbook for
her algebra class. The binder costs $9.25, the
textbook $32.50, the calculator $18.75, and the
workbook $15.00.
Find the total cost for Monica’s algebra supplies.
SOLUTION: To find the total cost for Monica’s Algebra supplies,
find the sum of the costs of the binder, the textbook,
the calculator and the workbook.
$9.25 + $32.50 + $18.75 + $15.00 = $75.50
So, the total cost for Monica’s Algebra supplies is
$75.50.
ANSWER: $75.50
Commutative (×)
Associative (×)
Substitution
Substitution
Use the Distributive Property to rewrite each
expression. Then evaluate.
37. (2 + 3)6
SOLUTION: 35. 5.3 + 2.8 + 3.7 + 6.2
SOLUTION: eSolutions Manual - Powered by Cognero
ANSWER: Commutative (+)
Associative (+)
Substitution
Substitution
ANSWER: 2(6) + 3(6); 30
38. 5(18 + 12)
SOLUTION: Page 5
ANSWER: Study
Guide
and
2(6)
+ 3(6);
30Review -Chapter 1
38. 5(18 + 12)
ANSWER: –2(5) – (–2)(3); –4
42. (8 – 3)4
SOLUTION: SOLUTION: ANSWER: 5(18) + 5(12); 150
ANSWER: 8(4) – 3(4); 20
39. 8(6 – 2)
SOLUTION: Rewrite each expression using the Distributive
Property. Then simplify.
43. 3(x + 2)
SOLUTION: ANSWER: 8(6) – 8(2); 32
ANSWER: 3(x) + 3(2); 3x + 6
40. (11 – 4)3
SOLUTION: 44. (m + 8)4
SOLUTION: ANSWER: 11(3) – 4(3); 21
41. –2(5 – 3)
SOLUTION: ANSWER: m(4) + 8(4); 4m + 32
45. 6(d − 3)
SOLUTION: ANSWER: 6(d) – 6(3); 6d – 18
ANSWER: –2(5) – (–2)(3); –4
46. –4(5 – 2t)
SOLUTION: 42. (8 – 3)4
SOLUTION: ANSWER: –4(5) – (–4)(2t); –20 + 8t
ANSWER: 8(4) – 3(4); 20
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Rewrite each expression using the Distributive
Property. Then simplify.
47. (9y – 6)(–3)
SOLUTION: Page 6
So, Mrs. Green gives 48 tutoring lessons in 4 weeks.
ANSWER: Study
Guide and Review -Chapter 1
–4(5) – (–4)(2t); –20 + 8t
ANSWER: 4(3 + 5 + 4); 48
Find the solution set of each equation if the
replacement sets are x: {1, 3, 5, 7, 9} and y: {6,
8, 10, 12, 14}
50. y – 9 = 3
47. (9y – 6)(–3)
SOLUTION: ANSWER: (9y)(–3) – (6)(–3); –27y + 18
SOLUTION: y
y–9=3
6
8
10
12
14
48. –6(4z + 3)
SOLUTION: True or
False?
False
False
6– 9=3
8– 9=3
10 – 9 = 3
12 – 9 = 3
14 – 9 = 3
False
True
False
The solution set is {12}.
ANSWER: –6(4z) + (–6)(3); –24z – 18
49. TUTORING Write and evaluate an expression for
the number of tutoring lessons Mrs. Green gives in 4
weeks.
ANSWER: {12}
51. 14 + x = 21
SOLUTION: x
14 + x =
21
1 14 + 1 = 21
3 14 + 3 = 21
5 14 + 5 = 21
7 14 + 7 = 21
9 14 + 9 = 21
SOLUTION: To find the number of tutoring lessons Mrs. Green
gives in 4 weeks, multiply 4 by the sum of the
number of students Mrs. Green tutors on Monday,
Tuesday, and Wednesday. So, the expression 4(3 + 5
+ 4) can be used to find the number of tutoring
lessons Mrs. Green gives in 4 weeks.
The solution set is {7}.
ANSWER: {7}
52. 4y = 32
SOLUTION: y
4y = 32
6
8
10
12
14
So, Mrs. Green gives 48 tutoring lessons in 4 weeks.
ANSWER: 4(3 + 5 + 4); 48
SOLUTION: eSolutions
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y–9=3
4(6) = 32
4(8) = 32
4(10) = 32
4(12) = 32
4(14) = 32
True or
False?
False
True
False
False
False
Find the solution set of each equation if the
replacement sets are x: {1, 3, 5, 7, 9} and y: {6,
8, 10, 12, 14}
50. y – 9 = 3
y
True or
False?
False
False
False
True
False
True or
False?
The solution set is {8}.
ANSWER: {8}
53. 3x – 11 = 16
SOLUTION: x
3x – 11 = 16
Page 7
True or
The solution set is {8}.
The solution set is {6}.
ANSWER: Study
Guide and Review -Chapter 1
{8}
53. 3x – 11 = 16
55. 2(x – 1) = 8
SOLUTION: x
3x – 11 = 16
1
3
5
7
9
3(1) –
3(2) –
3(5) –
3(7) –
3(9) –
ANSWER: {6}
11 = 16
11 = 16
11 = 16
11 = 16
11 = 16
True or
False?
False
False
False
False
True
SOLUTION: x
2(x – 1) = 8
1
3
5
7
9
2(1 –
2(3 –
2(5 –
2(7 –
2(9 –
1) = 8
1) = 8
1) = 8
1) = 8
1) = 8
True or
False?
False
False
True
False
False
The solution set is {9}.
The solution set is {5}.
ANSWER: {9}
ANSWER: {5}
54. Solve each equation.
56. a = 24 – 7(3)
SOLUTION: y
6
True or
False?
True
8
False
10
False
12
False
14
False
SOLUTION: ANSWER: 3
2
57. z = 63 ÷ (3 – 2)
SOLUTION: The solution set is {6}.
ANSWER: {6}
55. 2(x – 1) = 8
SOLUTION: x
2(x – 1) = 8
1
3
5
7
9
2(1 – 1) = 8
2(3 – 1) = 8
2(5 – 1) = 8
2(7 – 1) = 8
2(9 – 1) = 8
True or
False?
False
False
True
False
False
The solution set is {5}.
ANSWER: {5}
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Solve each equation.
56. a = 24 – 7(3)
ANSWER: 9
58. AGE Shandra’s age is four more than three times
Sherita’s age. Write an equation for Shandra’s age.
Then solve the equation if Sherita’s is 3 years old.
SOLUTION: Let K = Sherita’s age.
Let E = Shandra’s age.
The words more than suggest addition and the word
times suggests multiplication. So, 3K + 4 = E. To find
Shandra’s age when Sherita is 3, replace the K in the
equation with 3 and solve for E.
Page 8
ANSWER: Study
Guide and Review -Chapter 1
9
58. AGE Shandra’s age is four more than three times
Sherita’s age. Write an equation for Shandra’s age.
Then solve the equation if Sherita’s is 3 years old.
SOLUTION: Let K = Sherita’s age.
Let E = Shandra’s age.
The words more than suggest addition and the word
times suggests multiplication. So, 3K + 4 = E. To find
Shandra’s age when Sherita is 3, replace the K in the
equation with 3 and solve for E.
Mapping: List the x-values in the domain and the yvalues in the range. Draw arrows from the x-values
in the domain to the corresponding y-values in the
range.
The domain is {1, 2, 3, 4}, and the range is {3, 4, 5,
6}.
ANSWER: So, Shandra is 13 years old.
ANSWER: 3K + 4 = E; 13
Express each relation as a table, a graph, and a
mapping. Then determine the domain and
range.
59. {(1, 3), (2, 4), (3, 5), (4, 6)}
SOLUTION: Table: Place the x-coordinates into the first column
of the table. Place the corresponding y-coordinates in
the second column of the table.
Graph: Graph each ordered pair on a coordinate
plane.
Mapping: List the x-values in the domain and the yvalues in the range. Draw arrows from the x-values
in the domain to the corresponding y-values in the
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D = {1, 2, 3, 4} R = {3, 4, 5, 6}
60. {(–1, 1), (0, –2), (3, 1), (4, –1)}
SOLUTION: Table: Place the x-coordinates into the first column
of the table. Place the corresponding y-coordinates in
the second column of the table.
Graph: Graph each ordered pair on a coordinate
plane.
Page 9
Mapping: List the x-values in the domain and the yvalues in the range. Draw arrows from the x-values
Graph: Graph each ordered pair on a coordinate
plane.
Study Guide and Review -Chapter 1
Mapping: List the x-values in the domain and the yvalues in the range. Draw arrows from the x-values
in the domain to the corresponding y-values in the
range.
Mapping: List the x-values in the domain and the yvalues in the range. Draw arrows from the x-values
in the domain to the corresponding y-values in the
range.
The domain is {–1, 0, 3, 4}, and the range is {–2, –1,
1}.
ANSWER: The domain is {–2, –1, 0}, and the range is {2, 3, 4}.
ANSWER: D = {–1, 0, 3, 4} R = {–2, –1, 1}
61. {(–2, 4), (–1, 3), (0, 2), (–1, 2)}
SOLUTION: Table: Place the x-coordinates into the first column
of the table. Place the corresponding y-coordinates in
the second column of the table.
Express the relation shown in each table,
mapping, or graph as a set of ordered pairs.
Graph: Graph each ordered pair on a coordinate
plane.
62. eSolutions Manual - Powered by Cognero
SOLUTION: To express the relation as a set of ordered pairs,
write the x-coordinates followed by the
Page 10
corresponding y-coordinates. So, the ordered pairs
are {(5, 3), (3, –1), (1, 2), (–1, 0)}.
and then multiply by 7.
Planted
Growing
50
50 ÷ 10 × 7 = 35
100
100 ÷ 10 × 7 = 70
150
150 ÷ 10 × 7 = 105
200
200 ÷ 10 × 7 = 140
Study Guide and Review -Chapter 1
Express the relation shown in each table,
mapping, or graph as a set of ordered pairs.
The domain is the number of seeds planted, {50, 100,
150, 200}. The range is the number of plants
growing, {35, 70, 105, 140}.
Graph the number of seeds planted on the x-axis and
the number of plants growing on the y-axis. Then,
graph the ordered pairs from the table.
62. SOLUTION: To express the relation as a set of ordered pairs,
write the x-coordinates followed by the
corresponding y-coordinates. So, the ordered pairs
are {(5, 3), (3, –1), (1, 2), (–1, 0)}.
ANSWER: {(5, 3), (3, –1), (1, 2), (–1, 0)}
ANSWER: 63. SOLUTION: To express the relation as a set of ordered pairs,
write the values in the domain as the x-coordinates
and the corresponding range values as the ycoordinates. So, the ordered pairs are {(–2, –2), (0, –
3), (2, –2), (2, 0), (4, –1)}.
ANSWER: {(–2, –2), (0, –3), (2, –2), (2, 0), (4, –1)}
64. GARDENING On average, 7 plants grow for every
10 seeds of a certain type planted. Make a table to
show the relation between seeds planted and plants
growing for 50, 100, 150, and 200 seeds. Then state
the domain and range and graph the relation.
SOLUTION: To find the number of plants that grow for a certain
number of seeds, divid the number of seeds by 10
and then multiply by 7.
Planted
Growing
50
50 ÷ 10 × 7 = 35
100
100 ÷ 10 × 7 = 70
150
150 ÷ 10 × 7 = 105
200
200 ÷ 10 × 7 = 140
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The domain is the number of seeds planted, {50, 100,
150, 200}. The range is the number of plants
Determine whether each relation is a function.
65. SOLUTION: A function is a relationship between input and output.
Page 11
In a function, there is exactly one output for each
input. So, this relation is a function.
input. For this function the x value of 6 has two
different y outputs: 3 and 0, so it is not a function.
Study Guide and Review -Chapter 1
Determine whether each relation is a function.
ANSWER: not a function
If f (x) = 2x + 4 and g(x) = x 2 – 3, find each
value.
68. f (–3)
SOLUTION: 65. SOLUTION: A function is a relationship between input and output.
In a function, there is exactly one output for each
input. So, this relation is a function.
ANSWER: function
ANSWER: –2
69. g(2)
SOLUTION: 66. SOLUTION: A function is a relationship between input and output.
In a function, there is exactly one output for each
input. So, this relation is a function.
ANSWER: function
ANSWER: 1
70. f (0)
SOLUTION: 67. {(8, 4), (6, 3), (4, 2), (2, 1), (6, 0)}
SOLUTION: A function is a relationship between input and output.
In a function, there is exactly one output for each
input. For this function the x value of 6 has two
different y outputs: 3 and 0, so it is not a function.
ANSWER: 4
71. g(–4)
ANSWER: not a function
SOLUTION: If f (x) = 2x + 4 and g(x) = x 2 – 3, find each
value.
68. f (–3)
SOLUTION: ANSWER: 13
72. f (m + 2)
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ANSWER: –2
SOLUTION: Page 12
ANSWER: Study
Guide and Review -Chapter 1
13
72. f (m + 2)
SOLUTION: ANSWER: 2
9p – 3
74. GRADES A teacher claims that the relationship
between number of hours studied for a test and test
score can be described by g(x) = 45 + 9x, where x
represents the number of hours studied. Graph this
function.
SOLUTION: To graph the function, first make a table of values.
ANSWER: 2m + 8
73. g(3p )
SOLUTION: ANSWER: 2
x
1
2
3
4
5
g(x) = 45 + 9x
g(1) = 45 + 9(1) = 54
g(2) = 45 + 9(2) = 63
g(3) = 45 + 9(3) = 72
g(4) = 45 + 9(4) = 81
g(5) = 45 + 9(5) = 90
Graph the hours studied, x, on the x-axis and the test
scores, g(x), on the y-axis. Then, graph the ordered
pairs in the table. Draw a line through the points.
9p – 3
74. GRADES A teacher claims that the relationship
between number of hours studied for a test and test
score can be described by g(x) = 45 + 9x, where x
represents the number of hours studied. Graph this
function.
SOLUTION: To graph the function, first make a table of values.
x
1
2
3
4
5
g(x) = 45 + 9x
g(1) = 45 + 9(1) = 54
g(2) = 45 + 9(2) = 63
g(3) = 45 + 9(3) = 72
g(4) = 45 + 9(4) = 81
g(5) = 45 + 9(5) = 90
ANSWER: Graph the hours studied, x, on the x-axis and the test
scores, g(x), on the y-axis. Then, graph the ordered
pairs in the table. Draw a line through the points.
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75. Identify the function graphed as linear or nonlinear.
Then estimate and interpret the intercepts of the
graph, any symmetry, where the function is positive,
negative, increasing, and decreasing, the x-coordinate
Page 13
of any relative extrema, and the end behavior of the
graph.
Study Guide and Review -Chapter 1
75. Identify the function graphed as linear or nonlinear.
Then estimate and interpret the intercepts of the
graph, any symmetry, where the function is positive,
negative, increasing, and decreasing, the x-coordinate
of any relative extrema, and the end behavior of the
graph.
SOLUTION: Linear or Nonlinear: The graph is not a line, so the
function is nonlinear.
y-Intercept: The graph intersects the y-axis at
about (0, 56), so the y-intercept is about 5.6. This
means that about 56,000 U.S. patents were granted
in 1980.
x-Intercept: The graph does not intersect the xaxis, so there is no x-intercept. This means that in no
year were 0 patents granted.
Symmetry: The graph has no line symmetry.
Positive/Negative: The function is positive for all
values of x, so the number of patents will always
have a positive value.
Increasing/Decreasing: The function is increasing
for all values of x.
Extrema: The y-intercept is a relative minimum, so
the number of patents granted was at its lowest in
1980.
End Behavior: As x increases, y increases. As x
decreases, y decreases.
ANSWER: Nonlinear; the graph intersects the y-axis at about (0,
56), so the y-intercept is about 56. This means that
about 56,000 U.S. patents
were granted in 1980. The graph has no symmetry.
The graph does not intersect the x-axis, so there is no
x-intercept. This means that in
no year were 0 patents granted. The function is positive for all values of x, so the
number of patents will always have a positive value.
The function is increasing for all values of x. The yintercept is a relative minimum, so the number of
patents granted was at its lowest in 1980. As x
increases, y increases. As x decreases, y decreases.
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