College algebra : concepts and contexts / James Stewart, Lothar Redlin, Saleem Watson, Phyllis Panman. [print]

1. DATA, FUNCTIONS, AND MissouriDELS Making sense of data Analyzing one-variable data analyzing two-variable data Visualizing relationships in data Relations: input and output Graphing two-variable data in a coordinate plane Reading a Graph Equations : describing relationships in data Making a linear model from data Getting information from a linear model Functions : describing change Definition of function Which two-variable data represent functions? ; Which equations represent functions? ; Which graphs represent functions? ; Four ways to represent a function Function notation : the concept of function as a rule Function notation Evaluating Functions-net change The domain of a function Piecewise defined functions Working with functions : graphs and graphing calculators Graphing a function from a verbal description Graphs of basic functions Graphing with a graphing calculator Graphing piecewise defined functions Working with functions : getting information from the graph Reading the graph of a function Domain and range from a graph Increasing and decreasing functions Local maximum and minimum values Working with functions : modeling real-world relationships Modeling with functions Getting information from the graph of a model Making and using formulas What is a formula? Finding formulas Variables with subscripts Reading and using formulas Explorations Bias in presenting data Collecting and analyzing data Every graph tells a story.

2. LINEAR FUNCTIONS AND MissouriDELS Working with functions : average rate of change Average rate of change of a function Average speed of a moving object Functions defined by algebraic expressions Linear functions : constant rate of change Linear functions Linear functions and rate of change Linear functions and slope Using slope and rate of change Equations of lines : making linear models Slope-intercept form Point-slope form Horizontal and vertical lines When is the graph of an equation a line? Varying the coefficients : direct proportionality Varying the constant coefficient: parallel lines varying the coefficient of x: perpendicular lines Modeling direct proportionality Linear regression : fitting lines to data The line that best fits the data Using the line of best fit for prediction How good is the fit? the correlation coefficient Linear equations : getting information from a model Getting information from a linear model Models that lead to linear equations Linear equations : where lines meet Where lines meet Modeling supply and demand Explorations When rates of change change Linear patterns Bridge science Correlation and causation Fair division of assets.

3. EXPONENTIAL FUNCTIONS AND MissouriDELS Exponential growth and decay An example of exponential growth Modeling exponential growth: the growth factor Modeling exponential growth: the growth rate Modeling exponential decay Exponential models : comparing rates Changing the time period Growth of an investment: compound interest Comparing linear and exponential growth Average rate of change and percentage rate of change Comparing linear and exponential growth Logistic growth: growth with limited resources Graphs of exponential functions Graphs of exponential functions The effect of varying a or c Finding an exponential Function from a graph Fitting exponential curves to data Finding exponential models for data Is an exponential model appropriate? ; Modeling logistic growth Explorations extreme numbers-scientific notation so you want to be a millionaire? ; exponential patterns modeling radioactivity with coins and dice .

4. LOGARITHMIC FUNCTIONS AND EXPONENTIAL MissouriDELS Logarithmic functions Logarithms base 10 Logarithms base a Basic properties of logarithms Logarithmic functions and their graphs Laws of logarithms Laws of logarithms Expanding and combing logarithmic expressions Change of base formula Logarithmic scales Logarithmic scales The ph scale The decibel scale The richter scale The natural exponential and logarithmic functions What is the number e? ; The natural exponential and logarithmic functions Continuously compounded interest Instantaneous rates of growth or decay Expressing exponential models in terms of e Exponential equations : getting information from a model Solving exponential and logarithmic equations Getting information from exponential models: population and investment Getting information from exponential models:newton's law of cooling Finding the age of ancient objects: radiocarbon dating Working with functions : composition and inverse Functions o functions Reversing the rule of a function Which functions have inverses? Exponential and logarithmic functions as inverse functions Explorations super origami orders of magnitude semi-log graphs the even-tempered clavier.

5. QUADRATIC FUNCTIONS AND MissouriDELS Working with functions : shifting and stretching Shifting graphs up and down Shifting graphs left and right Stretching and shrinking graphics vertically Reflecting graphs Quadratic functions and their graphs ; The squaring function Quadratic functions in general form Quadratic functions in standard form Graphing using the standard form Maxima and minima : getting information from a model Finding maximum and minimum values Modeling with quadratic functions Quadratic equations : getting information from a model Solving quadratic equations: factoring Solving quadratic equations: the quadratic formula The discriminant Modeling with quadratic functions Fitting quadratic curves to data Modleing data with quadratic functions Explorations transformation stories Toricelli's law quadratic patterns.

6. POWER, POLYNOMIAL, AND RATIONAL FUNCTIONS Working with functions : algebraic operations Adding and subtracting functions multiplying and dividing functions Power functions : positive powers Power functions with positive integer powers Direct proportionality Fractional positive powers Modeling with power functions Polynomial functions : combining power functions Polynomial functions Graphing polynomial functions by factoring End behavior and the leading term Modeling with polynomial functions Fitting power and polynomial curves to data Fitting power curves to data A linear, power, or exponential model? ; Fitting polynomial curves to data Power functions : negative powers The reciprocal function Inverse proportionality Inverse square laws Rational functions Graphing quotients of linear functions Graphing rational functions Explorations only in the movies? ; proportionality-shape and size; managing traffic alcohol and the surge function.

7. SYSTEMS OF EQUATIONS AND DATA Indiana CaliforniaTEGORIES Systems of linear equations in two variables Systems of equations and their solutions The substitution method The elimination method Graphical interpretation: the number of solutions Applications: how much gold is in the crown? Systems of linear equations in several variables Solving a linear system Inconsistent and dependent systems Modeling with linear systems Using matrices to solve systems of linear equations Matrices The augmented matrix of a linear system Elementary row operations Row-echelon form Reduced row-echelon form Inconsistent and dependent systems Matrices and data in categories ; Organizing categorical data in a matrix Adding matrices Scalar multiplication of matrices Multiplying a matrix times a column matrix Matrix operations : getting information from data Addition, subtraction, and scalar multiplication Matrix multiplication Getting information from categorical data Matrix equations : solving a linear system The inverse of a matrix Matrix equations Modeling with matrix equations Explorations collecting categorical data will the species survive?.

Algebra toolkit A : working with numbers numbers and their properties the number line and intervals integer exponents; radicals and rational exponents Algebra toolkit B : working with expressions combining algebraic expressions factoring algebraic expressions rational expressions Algebra toolkit C : working with equations solving basic equations solving quadratic equations solving inequalities Algebra toolkit D : working with graphs the coordinate plane graphs of two-variable equations using a graphing calculator solving equations and inequalities graphically.

This textbook presents graphic, numeric and analytic approaches to the study of precalculus concepts from college algebra. It includes application of appropriate technology including graphing calculators to model, analyze and interpret a collection of data or to solve real-world application problems from a variety of disciplines. Topics include: the real number system; algebraic, exponential and logarithmic functions and their inverses; graphing techniques for polynomial and rational functions; complex numbers; theory of equations; partial fractions; mathematical induction; sequences and series; matrices; and the binomial theorem.

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