College Algebra: An Early Functions Approach, 4th edition — by Robert Blitzer | Instructor's Solutions Manual (All Chapters)

INSTRUCTOR’S
SOLUTIONS MANUAL
College Algebra: An Early Functions Approach, 4th edition
by Robert Blitzer
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, Table of Content
P. Prerequisites: Fundamental Concepts of Algebra
P.1 Algebraic Expressions, Mathematical Models, and Real Numbers
P.2 Basic Rules of Algebra
P.3 Exponents and Scientific Notation
P.4 Radicals and Rational Exponents
P.5 Polynomials
P.6 Factoring Polynomials
P.7 Rational Expressions
1. Functions and Graphs
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1.1 Graphs and Graphing Utilities
1.2 Basics of Functions and Their Graphs
1.3 More on Functions and Their Graphs
1.4 Linear Functions and Slope
1.5 More on Slope
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1.6 Transformations of Functions
1.7 Combinations of Functions; Composite Functions
1.8 Inverse Functions
1.9 Distance and Midpoint Formulas; Circles
2. Equations and Inequalities
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2.1 Linear Equations and Rational Equations
2.2 Models and Applications
2.3 Complex Numbers
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2.4 Quadratic Equations
2.5 Other Types of Equations
2.6 Linear Inequalities and Absolute Value Inequalities
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3. Polynomial and Rational Functions
3.1 Quadratic Functions
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3.2 Polynomial Functions and Their Graphs
3.3 Dividing Polynomials; Remainder and Factor Theorems
3.4 Zeros of Polynomial Functions
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3.5 Rational Functions and Their Graphs
3.6 Polynomial and Rational Inequalities
3.7 Modeling Using Variation
4. Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Properties of Logarithms
4.4 Exponential and Logarithmic Equations
4.5 Exponential Growth and Decay; Modeling Data
5. Systems of Equations and Inequalities

,5.1 Systems of Linear Equations in Two Variables
5.2 Systems of Linear Equations in Three Variables
5.3 Partial Fractions
5.4 Systems of Nonlinear Equations in Two Variables
5.5 Systems of Inequalities
5.6 Linear Programming
6. Matrices and Determinants
6.1 Matrix Solutions to Linear Systems
6.2 Inconsistent and Dependent Systems and Their Applications
6.3 Matrix Operations and Their Applications
6.4 Multiplicative Inverses of Matrices and Matrix Equations
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6.5 Determinants and Cramer's Rule
7. Conic Sections
7.1 The Ellipse
7.2 The Hyperbola
7.3 The Parabola
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8. Sequences, Induction, and Probability
8.1 Sequences and Summation Notation
8.2 Arithmetic Sequences
8.3 Geometric Sequences and Series
8.4 Mathematical Induction
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8.5 The Binomial Theorem
8.6 Counting Principles, Permutations, and Combinations
8.7 Probability
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, Chapter P
Fundamental Concepts of Algebra

Section P.1

Check Point Exercises

1. 8 + 6( x − 3) 2 = 8 + 6(13 − 3) 2
= 8 + 6(10) 2
= 8 + 6(100)
= 8 + 600
= 608
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2. a. Since 2014 is 14 years after 2000, substitute 14 for x.
T = 4 x 2 + 330 x + 3310
= 4(14) 2 + 330(14) + 3310
= 8714
The average cost of tuition and fees at public U.S. colleges for the school year ending in 2014 was $8714.
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b. The formula underestimates the actual answer by $179.
3. The elements common to {3, 4, 5, 6, 7} and {3, 7, 8, 9} are 3 and 7.
{3, 4,5, 6, 7} ∩ {3, 7,8,9} = {3, 7}

4. The union is the set containing all the elements of either set.
{3, 4,5, 6, 7} ∪ {3, 7,8,9} = {3, 4,5, 6, 7,8,9}
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5. −9, − 1.3, 0, 0.3, , 9, 10 
 2 
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a. Natural numbers: 9 because 9 =3

b. Whole numbers: 0, 9

c. Integers: −9, 0, 9
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d. Rational numbers: −9, − 1.3, 0, 0.3, 9

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e. Irrational numbers: , 10
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f. Real numbers: −9, − 1.3, 0, 0.3, , 9, 10
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6. a. [−2, 5) = { x −2 ≤ x < 5}



b. [1, 3.5] = { x 1 ≤ x ≤ 3.5}



c. [−∞, − 1) = { x x < −1}




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