9780395692837

Algebra for College Students

by
  • ISBN13:

    9780395692837

  • ISBN10:

    0395692830

  • Format: Hardcover
  • Publisher: Houghton Mifflin Company
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Table of Contents

Preface xv
To the Student xxv
Equations and Inequalities
1(76)
Variable Expressions
3(19)
Properties of Real Numbers
3(3)
Set operations and interval notation
6(5)
Evaluate variable expressions
11(2)
Simplify variable expressions
13(1)
Simplify radical expressions
14(2)
Translate verbal expressions into variable expressions
16(6)
Equations
22(14)
Solve equations using the Addition and Multiplication Properties of Equations
22(4)
Solve equations using the Distributive Property
26(2)
Literal equations
28(1)
Application problems
29(7)
Value Mixture and Uniform Motion Problems
36(7)
Value mixture problems
36(2)
Uniform motion problems
38(5)
Application Problems Involving Percent
43(8)
Investment problems
43(2)
Percent mixture problems
45(6)
Inequalities in One Variable
51(9)
Solve inequalities in one variable
51(3)
Solve compound inequalities
54(2)
Application problems
56(4)
Absolute Value Equations and Inequalities
60(17)
Absolute value equations
60(4)
Absolute value inequalities
64(2)
Application problems
66(4)
Something Extra
70(1)
Chapter Summary
71(3)
Chapter Review Exercises
74(3)
Linear Functions and Inequalities in Two variables
77(82)
The Rectangular Coordinate System
79(10)
Plot points in a rectangular coordinate system
79(3)
Distance and midpoint formulas
82(3)
Scatter diagrams
85(4)
Introduction to Functions
89(15)
Evaluate a function
89(5)
Find the domain and range of a function
94(3)
Determine whether or not a relation is a function
97(7)
Linear Functions
104(10)
Graph an equation of the form f(x) = mx + b or y = mx + b
104(5)
Find the x- and y-intercepts of a straight line
109(5)
Slope of a Straight Line
114(11)
Find the slope of a line given two points
114(2)
Graph a line given a point and the slope
116(9)
Equations of Straight Lines and Their Inverses
125(15)
Find the equation of a line given a point and the slope or given two points
125(2)
Find the equations of parallel and perpendicular lines
127(4)
Find the inverse of a linear function
131(9)
Inequalities in Two Variables
140(3)
Graph the solution set of an inequality in two variables
140(3)
Applications of Linear Functions
143(16)
Application problems
143(8)
Something Extra
151(1)
Chapter Summary
152(2)
Chapter Review Exercises
154(2)
Cumulative Review Exercises
156(3)
Polynomials and Polynomial Functions
159(74)
Exponential Expressions
161(12)
Multiply monomials
161(2)
Simplify expressions containing integer exponents
163(4)
Scientific notation
167(2)
Application problems
169(4)
Introduction to Polynomials
173(11)
Polynomial functions
173(3)
Graphs and zeros of polynomial functions
176(2)
Add and subtract polynomials
178(6)
Multiplication of Polynomials
184(9)
Multiply a polynomial by a monomial
184(1)
Multiply polynomials
184(4)
Application problems
188(5)
Division of Polynomials
193(8)
Divide polynomials
193(2)
Synthetic division, the Remainder Theorem, and the Factor Theorem
195(6)
Factoring Polynomials
201(11)
Factor a monomial from a polynomial
201(1)
Factor by grouping
202(2)
Factor trinomials of the form x2 + bx + c
204(2)
Factor trinomials of the form ax2 + bx + c
206(6)
Special Factoring
212(7)
Factor the difference of two perfect squares and perfect square trinomials
212(1)
Factor the sum or the difference of two cubes
213(2)
Factor trinomials that are quadratic in form
215(1)
Factor completely
216(3)
Solving Equations by Factoring
219(14)
Solve equations by factoring
219(3)
Application problems
222(4)
Something Extra
226(1)
Chapter Summary
227(2)
Chapter Review Exercises
229(1)
Cumulative Review Exercises
230(3)
Rational Exponents and Radical Expressions
233(46)
Rational Exponents and Radical Expressions
235(11)
Simplify expressions with rational exponents
235(2)
Write equivalent exponential and radical expressions
237(2)
Simplify radical expressions
239(7)
Operations on Radical Expressions
246(7)
Add and subtract radical expressions
246(1)
Multiply radical expressions
247(1)
Divide radical expressions
248(5)
Complex Numbers
253(9)
Simplify complex numbers
253(2)
Add and subtract complex numbers
255(1)
Multiply and divide complex numbers
256(6)
Radical Functions
262(4)
Find the domain of a radical function
262(1)
Graph a radical function
263(3)
Equations Containing Radical Expressions
266(13)
Solve equations containing radical expressions
266(3)
Application problems
269(4)
Something Extra
273(1)
Chapter Summary
274(1)
Chapter Review Exercises
275(1)
Cumulative Review Exercises
276(3)
Quadratic Functions and Inequalities
279(48)
Solving Quadratic Equations by Factoring or by Taking Square Roots
281(6)
Solve quadratic equations by factoring
281(1)
Write a quadratic equation given its solutions
282(1)
Solve quadratic equations by taking square roots
283(4)
Solving Quadratic Equations by Completing the Square and by Using the Quadratic Formula
287(9)
Solve quadratic equations by completing the square
287(3)
Solve quadratic equations by using the quadratic formula
290(6)
Equations That Are Reducible to Quadratic Equations
296(7)
Equations that are quadratic in form
296(2)
Radical equations
298(1)
Fractional equations
299(4)
Graphing Quadratic Functions
303(11)
Graph a quadratic function
303(5)
Find the x-intercepts of a parabola
308(6)
Applications of Quadratic Equations
314(4)
Minimum and maximum problems
314(4)
Nonlinear Inequalities
318(9)
Solve inequalities by factoring
318(3)
Something Extra
321(1)
Chapter Summary
322(1)
Chapter Review Exercises
323(2)
Cumulative Review Exercises
325(2)
Rational Functions and Expressions
327(56)
Introduction to Rational Functions
329(7)
Find the domain of a rational function
329(2)
Simplify rational expressions
331(5)
Operations on Rational Expressions
336(10)
Multiply and divide rational expressions
336(2)
Add and subtract rational expressions
338(8)
Complex Fractions
346(6)
Simplify complex fractions
346(6)
Rational Equations and Inequalities
352(5)
Solve rational equations
352(2)
Solve rational inequalities
354(3)
Applications of Rational Equations
357(10)
Work problems
357(2)
Uniform motion problems
359(8)
Proportions and Variation
367(16)
Proportions
367(1)
Variation
368(8)
Something Extra
376(1)
Chapter Summary
377(1)
Chapter Review Exercises
378(3)
Cumulative Review Exercises
381(2)
Exponential and Logarithmic Functions
383(52)
The Exponential Function
385(8)
Evaluate exponential functions
385(2)
Graph exponential functions
387(6)
Introduction to Logarithms
393(13)
Write equivalent exponential and logarithmic equations
393(3)
The properties of logarithms
396(10)
Graphs of Logarithmic Functions
406(8)
Graph logarithmic functions
406(8)
Exponential and Logarithmic Equations
414(6)
Solve exponential equations
414(2)
Solve logarithmic equations
416(4)
Applications of Exponential and Logarithmic Functions
420(15)
Application problems
420(9)
Something Extra
429(2)
Chapter Summary
431(1)
Chapter Review Exercises
432(1)
Cumulative Review Exercises
433(2)
Conic Sections
435(26)
The Parabola
437(4)
Graph parabolas
437(4)
The Circle
441(5)
Graph circles
441(5)
The Ellipse and the Hyperbola
446(6)
Graph an ellipse with center at the origin
446(2)
Graph a hyperbola with center at the origin
448(4)
Quadratic Inequalities
452(9)
Graph the solution set of a quadratic inequality in two variables
452(2)
Something Extra
454(2)
Chapter Summary
456(1)
Chapter Review Exercises
457(1)
Cumulative Review Exercises
458(3)
Systems of Equations and Matrices
461(60)
Solving Systems of Linear Equations by Graphing and by the Substitution Method
463(8)
Solve systems of linear equations by graphing
463(3)
Solve systems of linear equations by the substitution method
466(5)
Solving Systems of Linear Equations by the Addition Method
471(10)
Solve systems of two linear equations in two variables by the addition method
471(3)
Solve systems of three linear equations in three variables by the addition method
474(7)
Solving Nonlinear Systems of Equations and Systems of Inequalities
481(8)
Solve nonlinear systems of equations
481(5)
Graph the solution set of a system of inequalities
486(3)
Solving Systems of Equations by using Matrices
489(9)
Solve systems of equations by using matrices
489(9)
Determinant of a Matrix
498(8)
Evaluate determinants
498(4)
Solve systems of equations by using Cramer's Rule
502(4)
Application Problems in Two Variables
506(15)
Rate-of-wind and water current problems
506(2)
Application problems
508(6)
Something Extra
514(2)
Chapter Summary
516(1)
Chapter Review Exercises
517(2)
Cumulative Review Exercises
519(2)
Sequences and Series
521(29)
Introduction to Sequences and Series
523(6)
Write the terms of a sequence
523(2)
Find the sum of a series
525(4)
Arithmetic Sequences and Series
529(8)
Find the nth term of an arithmetic sequence
529(3)
Find the sum of an arithmetic series
532(1)
Application problems
533(4)
Geometric Sequences and Series
537(9)
Find the nth term of a geometric sequence
537(2)
Finite geometric series
539(1)
Infinite geometric series
540(2)
Application problems
542(4)
Binomial Expansions
546
Expand (a + b)n
546(6)
Something Extra
552(1)
Chapter Summary
553(2)
Chapter Review Exercises
555(1)
Cumulative Review Exercises
556
APPENDIX
Tips for Graphing
A3
Solutions to Problems
A11
Answers to Odd-Numbered Exercises
A65
Index

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