INSTRUCTOR’S
SOLUTIONS MANUAL
for
TE
College Algebra with
ST
Corequisite Support, 5th
edition
SO
By Judith Beecher, Judith
LU
Penna
TI
(All Chapters 1-8, 100%
O
N
Original
Verified, A+ Grade)
, Table of Content
1. Graphs, Functions, and Models
1.1 Introduction to Graphing
1.2 Functions and Graphs
1.3 Linear Functions, Slope, and Applications
1.4 Equations of Lines and Modeling
1.5 Linear Equations, Functions, Zeros, and Applications
1.6 Solving Linear Inequalities
Integrated Review Topics:
Graphing Linear Functions
Operations on the Real Numbers
TE
Order of operations
Factoring trinomials: ax2 + bx + c
Factoring trinomial squares and differences of squares
The principle of zero products
Interval notation
ST
Solving linear equations
Solving linear inequalities
2. More on Functions
2.1 Increasing, Decreasing, and Piecewise Functions; Applications
2.2 The Algebra of Functions
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2.3 The Composition of Functions
2.4 Symmetry
2.5 Transformations
2.6 Variation and Applications
Integrated Review Topics:
Interval Notation
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The Pythagorean Theorem
Simplifying Rational expressions
Addition and subtraction of polynomials
Simplifying complex rational expressions
3. Quadratic Functions and Equations; Inequalities
3.1 The Complex Numbers
TI
3.2 Quadratic Equations, Functions, Zeros, and Models
3.3 Analyzing Graphs of Quadratic Functions
3.4 Solving Rational Equations and Radical Equations
O
3.5 Solving Equations and Inequalities with Absolute Value
Integrated Review Topics:
Multiplying radical expressions
N
Multiplying binomials
Simplifying radical expressions
Completing the square
Factoring trinomials: ax2 + bx + c
Factoring trinomial squares and differences of squares
The principle of zero products
Finding the LCM of algebraic expressions
The principle of powers
4. Polynomial Functions and Rational Functions
4.1 Polynomial Functions and Models
4.2 Graphing Polynomial Functions
,4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem
4.4 Theorems about Zeros of Polynomial Functions
4.5 Rational Functions
4.6 Polynomial Inequalities and Rational Inequalities
Integrated Review Topics:
Introduction to polynomials
Factoring by grouping
Operations on the Real Numbers
Interval Notation
5. Exponential Functions and Logarithmic Functions
5.1 Inverse Functions
5.2 Exponential Functions and Graphs
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5.3 Logarithmic Functions and Graphs
5.4 Properties of Logarithmic Functions
5.5 Solving Exponential Equations and Logarithmic Equations
5.6 Applications and Models: Growth and Decay; Compound Interest
Integrated Review Topics:
ST
Integers as exponents
Finding logarithms without a calculator
6. Systems of Equations and Matrices
6.1 Systems of Equations in Two Variables
6.2 Systems of Equations in Three Variables
SO
6.3 Matrices and Systems of Equations
6.4 Matrix Operations
6.5 Inverses of Matrices
6.6 Determinants and Cramer’s Rule
6.7 Systems of Inequalities and Linear Programming
6.8 Partial Fractions
LU
Integrated Review Topics:
Graphing Linear Functions
Operations on the Real Numbers
7. Conic Sections
7.1 The Parabola
7.2 The Circle and the Ellipse
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7.3 The Hyperbola
7.4 Nonlinear Systems of Equations and Inequalities
Integrated Review Topic:
O
Completing the square
8. Sequences, Series, and Combinatorics
8.1 Sequences and Series
8.2 Arithmetic Sequences and Series
N
8.3 Geometric Sequences and Series
8.4 Mathematical Induction
8.5 Combinatorics: Permutations
8.6 Combinatorics: Combinations
8.7 The Binomial Theorem
8.8 Probability
, Chapter 1
Graphs, Functions, and Models
4. y
Exercise Set 1.1
4 (1, 4)
1. Point A is located 5 units to the left of the y-axis and 2
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(5, 0) (4, 0)
4 units up from the x-axis, so its coordinates are (−5, 4). 4 2 2 4 x
Point B is located 2 units to the right of the y-axis and 2
(4, 2)
2 units down from the x-axis, so its coordinates are (2, −2). 4 (2, 4)
Point C is located 0 units to the right or left of the y-axis
and 5 units down from the x-axis, so its coordinates are
(0, −5). 5. To graph (−5, 1) we move from the origin 5 units to the
ST
left of the y-axis. Then we move 1 unit up from the x-axis.
Point D is located 3 units to the right of the y-axis and
5 units up from the x-axis, so its coordinates are (3, 5). To graph (5, 1) we move from the origin 5 units to the right
of the y-axis. Then we move 1 unit up from the x-axis.
Point E is located 5 units to the left of the y-axis and
4 units down from the x-axis, so its coordinates are To graph (2, 3) we move from the origin 2 units to the right
(−5, −4). of the y-axis. Then we move 3 units up from the x-axis.
Point F is located 3 units to the right of the y-axis and To graph (2, −1) we move from the origin 2 units to the
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0 units up or down from the x-axis, so its coordinates are right of the y-axis. Then we move 1 unit down from the
(3, 0). x-axis.
To graph (0, 1) we do not move to the right or the left of
2. G: (2, 1); H: (0, 0); I: (4, −3); J: (−4, 0); K: (−2, 3); the y-axis since the first coordinate is 0. From the origin
L: (0, 5) we move 1 unit up.
3. To graph (4, 0) we move from the origin 4 units to the right
y
of the y-axis. Since the second coordinate is 0, we do not
move up or down from the x-axis.
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4
To graph (−3, −5) we move from the origin 3 units to the (2, 3)
2
left of the y-axis. Then we move 5 units down from the (5, 1) (0, 1) (5, 1)
x-axis. 4 2 4 x
To graph (−1, 4) we move from the origin 1 unit to the left 2 (2, 1)
of the y-axis. Then we move 4 units up from the x-axis. 4
To graph (0, 2) we do not move to the right or the left of
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the y-axis since the first coordinate is 0. From the origin y
6.
we move 2 units up.
To graph (2, −2) we move from the origin 2 units to the 4
right of the y-axis. Then we move 2 units down from the (5, 2)
2
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x-axis. (5, 0) (4, 0)
4 2 2 4 x
y 2
4 (4, 3)
(1, 4) 4 (1, 5)
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2 (0, 2)
(4, 0) 7. The first coordinate represents the year and the second co-
4 2 2 4 x ordinate represents the number of Sprint Cup Series races
2 (2, 2)
in which Tony Stewart finished in the top five. The or-
(3, 5) 4 dered pairs are (2008, 10), (2009, 15), (2010, 9), (2011, 9),
(2012, 12), and (2013, 5).
8. The first coordinate represents the year and the second
coordinate represents the percent of Marines who are
women. The ordered pairs are (1960, 1%), (1970, 0.9%),
(1980, 3.6%), (1990, 4.9%), (2000, 6.1%), and (2011, 6.8%).
Copyright
c 2016 Pearson Education, Inc.
SOLUTIONS MANUAL
for
TE
College Algebra with
ST
Corequisite Support, 5th
edition
SO
By Judith Beecher, Judith
LU
Penna
TI
(All Chapters 1-8, 100%
O
N
Original
Verified, A+ Grade)
, Table of Content
1. Graphs, Functions, and Models
1.1 Introduction to Graphing
1.2 Functions and Graphs
1.3 Linear Functions, Slope, and Applications
1.4 Equations of Lines and Modeling
1.5 Linear Equations, Functions, Zeros, and Applications
1.6 Solving Linear Inequalities
Integrated Review Topics:
Graphing Linear Functions
Operations on the Real Numbers
TE
Order of operations
Factoring trinomials: ax2 + bx + c
Factoring trinomial squares and differences of squares
The principle of zero products
Interval notation
ST
Solving linear equations
Solving linear inequalities
2. More on Functions
2.1 Increasing, Decreasing, and Piecewise Functions; Applications
2.2 The Algebra of Functions
SO
2.3 The Composition of Functions
2.4 Symmetry
2.5 Transformations
2.6 Variation and Applications
Integrated Review Topics:
Interval Notation
LU
The Pythagorean Theorem
Simplifying Rational expressions
Addition and subtraction of polynomials
Simplifying complex rational expressions
3. Quadratic Functions and Equations; Inequalities
3.1 The Complex Numbers
TI
3.2 Quadratic Equations, Functions, Zeros, and Models
3.3 Analyzing Graphs of Quadratic Functions
3.4 Solving Rational Equations and Radical Equations
O
3.5 Solving Equations and Inequalities with Absolute Value
Integrated Review Topics:
Multiplying radical expressions
N
Multiplying binomials
Simplifying radical expressions
Completing the square
Factoring trinomials: ax2 + bx + c
Factoring trinomial squares and differences of squares
The principle of zero products
Finding the LCM of algebraic expressions
The principle of powers
4. Polynomial Functions and Rational Functions
4.1 Polynomial Functions and Models
4.2 Graphing Polynomial Functions
,4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem
4.4 Theorems about Zeros of Polynomial Functions
4.5 Rational Functions
4.6 Polynomial Inequalities and Rational Inequalities
Integrated Review Topics:
Introduction to polynomials
Factoring by grouping
Operations on the Real Numbers
Interval Notation
5. Exponential Functions and Logarithmic Functions
5.1 Inverse Functions
5.2 Exponential Functions and Graphs
TE
5.3 Logarithmic Functions and Graphs
5.4 Properties of Logarithmic Functions
5.5 Solving Exponential Equations and Logarithmic Equations
5.6 Applications and Models: Growth and Decay; Compound Interest
Integrated Review Topics:
ST
Integers as exponents
Finding logarithms without a calculator
6. Systems of Equations and Matrices
6.1 Systems of Equations in Two Variables
6.2 Systems of Equations in Three Variables
SO
6.3 Matrices and Systems of Equations
6.4 Matrix Operations
6.5 Inverses of Matrices
6.6 Determinants and Cramer’s Rule
6.7 Systems of Inequalities and Linear Programming
6.8 Partial Fractions
LU
Integrated Review Topics:
Graphing Linear Functions
Operations on the Real Numbers
7. Conic Sections
7.1 The Parabola
7.2 The Circle and the Ellipse
TI
7.3 The Hyperbola
7.4 Nonlinear Systems of Equations and Inequalities
Integrated Review Topic:
O
Completing the square
8. Sequences, Series, and Combinatorics
8.1 Sequences and Series
8.2 Arithmetic Sequences and Series
N
8.3 Geometric Sequences and Series
8.4 Mathematical Induction
8.5 Combinatorics: Permutations
8.6 Combinatorics: Combinations
8.7 The Binomial Theorem
8.8 Probability
, Chapter 1
Graphs, Functions, and Models
4. y
Exercise Set 1.1
4 (1, 4)
1. Point A is located 5 units to the left of the y-axis and 2
TE
(5, 0) (4, 0)
4 units up from the x-axis, so its coordinates are (−5, 4). 4 2 2 4 x
Point B is located 2 units to the right of the y-axis and 2
(4, 2)
2 units down from the x-axis, so its coordinates are (2, −2). 4 (2, 4)
Point C is located 0 units to the right or left of the y-axis
and 5 units down from the x-axis, so its coordinates are
(0, −5). 5. To graph (−5, 1) we move from the origin 5 units to the
ST
left of the y-axis. Then we move 1 unit up from the x-axis.
Point D is located 3 units to the right of the y-axis and
5 units up from the x-axis, so its coordinates are (3, 5). To graph (5, 1) we move from the origin 5 units to the right
of the y-axis. Then we move 1 unit up from the x-axis.
Point E is located 5 units to the left of the y-axis and
4 units down from the x-axis, so its coordinates are To graph (2, 3) we move from the origin 2 units to the right
(−5, −4). of the y-axis. Then we move 3 units up from the x-axis.
Point F is located 3 units to the right of the y-axis and To graph (2, −1) we move from the origin 2 units to the
SO
0 units up or down from the x-axis, so its coordinates are right of the y-axis. Then we move 1 unit down from the
(3, 0). x-axis.
To graph (0, 1) we do not move to the right or the left of
2. G: (2, 1); H: (0, 0); I: (4, −3); J: (−4, 0); K: (−2, 3); the y-axis since the first coordinate is 0. From the origin
L: (0, 5) we move 1 unit up.
3. To graph (4, 0) we move from the origin 4 units to the right
y
of the y-axis. Since the second coordinate is 0, we do not
move up or down from the x-axis.
LU
4
To graph (−3, −5) we move from the origin 3 units to the (2, 3)
2
left of the y-axis. Then we move 5 units down from the (5, 1) (0, 1) (5, 1)
x-axis. 4 2 4 x
To graph (−1, 4) we move from the origin 1 unit to the left 2 (2, 1)
of the y-axis. Then we move 4 units up from the x-axis. 4
To graph (0, 2) we do not move to the right or the left of
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the y-axis since the first coordinate is 0. From the origin y
6.
we move 2 units up.
To graph (2, −2) we move from the origin 2 units to the 4
right of the y-axis. Then we move 2 units down from the (5, 2)
2
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x-axis. (5, 0) (4, 0)
4 2 2 4 x
y 2
4 (4, 3)
(1, 4) 4 (1, 5)
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2 (0, 2)
(4, 0) 7. The first coordinate represents the year and the second co-
4 2 2 4 x ordinate represents the number of Sprint Cup Series races
2 (2, 2)
in which Tony Stewart finished in the top five. The or-
(3, 5) 4 dered pairs are (2008, 10), (2009, 15), (2010, 9), (2011, 9),
(2012, 12), and (2013, 5).
8. The first coordinate represents the year and the second
coordinate represents the percent of Marines who are
women. The ordered pairs are (1960, 1%), (1970, 0.9%),
(1980, 3.6%), (1990, 4.9%), (2000, 6.1%), and (2011, 6.8%).
Copyright
c 2016 Pearson Education, Inc.
