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Available4.4
21 reviews
ISBN 10: 113396074X
ISBN 13: 9781133960744
Author: Ron Larson, Robert P Hostetler
With the same design and feature sets as the market leading Precalculus, Ninth Edition, this concise text provides both students and instructors with sound, consistently structured explanations of the mathematical concepts. PRECALCULUS: A CONCISE COURSE is designed to offer a cost-effective, one-semester alternative to the traditional two-semester precalculus text. It contains the features that have made the Larson series a complete solution for both students and instructors: interesting applications, pedagogically effective design, and innovative technology combined with an abundance of carefully developed examples with worked-out solutions and exercises.
Chapter 1. Functions and Their Graphs
1.1. Rectangular Coordinates
The Cartesian Plane
The Pythagorean Theorem and the Distance Formula
The Midpoint Formula
Applications
Exercises
1.2. Graphs of Equations
The Graph of an Equation
Intercepts of a Graph
Symmetry
Circles
Application
Exercises
1.3. Linear Equations in Two Variables
Using Slope
Finding the Slope of a Line
Writing Linear Equations in Two Variables
Parallel and Perpendicular Lines
Applications
Exercises
1.4. Functions
Introduction to Functions and Function Notation
The Domain of a Function
Applications
Difference Quotients
Exercises
1.5. Analyzing Graphs of Functions
The Graph of a Function
Zeros of a Function
Increasing and Decreasing Functions
Average Rate of Change
Even and Odd Functions
Exercises
1.6. A Library of Parent Functions
Linear and Squaring Functions
Cubic, Square Root, and Reciprocal Functions
Step and Piecewise-Defined Functions
Parent Functions
Exercises
1.7. Transformations of Functions
Shifting Graphs
Reflecting Graphs
Nonrigid Transformations
Exercises
1.8. Combinations of Functions: Composite Functions
Arithmetic Combinations of Functions
Composition of Functions
Application
Exercises
1.9. Inverse Functions
Inverse Functions
The Graph of an Inverse Function
One-to-One Functions
Finding Inverse Functions Algebraically
Exercises
1.10. Mathematical Modeling and Variation
Introduction
Least Squares Regression and Graphing Utilities
Direct Variation
Direct Variation as an n th Power
Inverse Variation
Combined Variation
Joint Variation
Exercises
Chapter Summary
Review Exercises
Chapter Test
Proofs in Mathematics
P.S. Problem Solving
Chapter 2. Polynomial and Rational Functions
2.1. Quadratic Functions and Models
The Graph of a Quadratic Function
The Standard Form of a Quadratic Function
Finding Minimum and Maximum Values
Exercises
2.2. Polynomial Functions of Higher Degree
Graphs of Polynomial Functions
The Leading Coefficient Test
Real Zeros of Polynomial Functions
The Intermediate Value Theorem
Exercises
2.3. Polynomial and Synthetic Division
Long Division of Polynomials
Synthetic Division
The Remainder and Factor Theorems
Exercises
2.4. Complex Numbers
The Imaginary Unit i
Operations with Complex Numbers
Complex Conjugates
Complex Solutions of Quadratic Equations
Exercises
2.5. Zeros of Polynomial Functions
The Fundamental Theorem of Algebra
The Rational Zero Test
Conjugate Pairs
Factoring a Polynomial
Other Tests for Zeros of Polynomials
Application
Exercises
2.6. Rational Functions
Introduction
Vertical and Horizontal Asymptotes
Sketching the Graph of a Rational Function
Slant Asymptotes
Applications
Exercises
2.7. Nonlinear Inequalities
Polynomial Inequalities
Rational Inequalities
Applications
Exercises
Chapter Summary
Review Exercises
Chapter Test
Proofs in Mathematics
P.S. Problem Solving
Chapter 3. Exponential and Logarithmic Functions
3.1. Exponential Functions and Their Graphs
Exponential Functions
Graphs of Exponential Functions
The Natural Base e
Applications
Exercises
3.2. Logarithmic Functions and Their Graphs
Logarithmic Functions
Graphs of Logarithmic Functions
The Natural Logarithmic Function
Application
Exercises
3.3. Properties of Logarithms
Change of Base
Properties of Logarithms
Rewriting Logarithmic Expressions
Application
Exercises
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