# Mathematics in Action: Algebraic, Graphical, and Trigonometric Problem Solving

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## 0321149203

• Edition: 2nd
• Format: Package
• Publisher: Addison Wesley
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### Summary

This intermediate algebra text, based on standards in the AMATYC Crossroads document, motivates college math students to develop mathematical literacy and a solid foundation for future study in mathematics and other disciplines. This third book of a three-book series presents mathematical concepts and skills through relevant activities derived from real-life situations. These activities are meaningful to students because they illustrate how mathematics arises naturally from real-world situations and problems. The Mathematics in Action series is based on the assumption that students learn mathematics best by doing mathematics in a meaningful context. Therefore, the text takes a collaborative approach to learning. Students take an active role in their own learning by working in groups, thereby developing communication skills, a sense of independence, and a can-do attitude about mathematics. Technology is integrated throughout the book so that students learn to interpret real-life data numerically, symbolically, and graphically. Regardless of their level of preparation for the course, students can use this text to increase their knowledge of mathematics, their problem-solving skills, and their overall confidence in their ability to learn.

Preface xiii
 Function Sense
1(180)
 Modeling with Functions
1(42)
 Parking Problems
1(12)
 Distinguish between input and output
 Define a function
 Represent a function numerically and graphically
 Write a function using function notation
 Fill 'er Up
13(10)
 Objectives: Determine the equation (symbolic representation) that defines a function
 Write the equation to define a function
 Determine the domain and range of a function
 Identify the independent and the dependent variables of a function
 Stopping Short
23(9)
 Use a function as a mathematical model
 Determine when a function is increasing, decreasing, or constant
 Use the vertical line test to determine if a graph represents a function
 Graphs Tell Stories
32(4)
 Describe in words what a graph tells you about a given situation
 Sketch a graph that best represents the situation described in words
 What Have I Learned?
36(1)
 How Can I Practice?
37(6)
 Linear Functions
43(53)
 Walking for Fitness
43(8)
 Determine the average rate of change
 Depreciation
51(12)
 Interpret slope as an average rate of change
 Use the formula to determine slope
 Discover the practical meaning of vertical and horizontal intercepts
 Develop the slope/intercept form of an equation of a line
 Use the slope/intercept formula to determine vertical and horizontal intercepts
 A Visit to the Architect
63(10)
 Determine the slope-intercept form of a line given the slope and vertical intercept
 Determine the slope-intercept form of a line given two points on the line
 Compare the slopes of parallel lines
 Skateboard Heaven
73(9)
 Write an equation of a line in general form Ax + By = C
 Write the slope-intercept form of a linear equation given the general form
 College Tuition
82(6)
 Determine a line of best fit with a straightedge
 Determine the equation of a regression line using a graphing calculator
 Use the regression equation to interpolate and extrapolate
 What Have I Learned?
88(2)
 How Can I Practice?
90(6)
 Systems of Linear Equations, Inequalities, and Absolute Value Functions
96(85)
 Ride for Less
96(13)
 Solve a system of 2 X 2 linear equations numerically and graphically
 Solve a system of 2 X 2 linear equations using the substitution method
 Solve an equation of the form ax + b = cx + d for x
 Healthy Lifestyle
109(7)
 Solve a 2 X 2 linear system algebraically using the substitution method and the addition method
 Solve equations containing parentheses
 Sam's Cafe
116(5)
 Solve a 3 X 3 linear system of equations
 How Long Can You Live?
121(13)
 Solve linear inequalities numerically and graphically
 Use properties of inequalities to solve linear inequalities algebraically
 Solve compound inequalities algebraically and graphically
 Long Distance by Phone
134(10)
 Objectives: Graph a piecewise linear function
 Write a piecewise linear function to represent a given situation
 Graph a function defined by y = |x -- c|
 How Much Can You Tolerate?
144(12)
 Write a compound inequality to represent a given statement
 Determine the error
 Solve an equation involving absolute value using a number line
 Solve an inequality involving absolute value using a number line
 Solve absolute value equations and inequalities using a graphing approach
 Interpret absolute value as distance
 Graph an absolute value function
 What Have I Learned?
156(2)
 How Can I Practice?
158(5)
 Chapter 1 Summary
163(6)
 Chapter 1 Gateway Review
169(12)
 The Algebra of Functions
181(102)
 Addition, Subtraction, and Multiplication of Polynomial Functions
181(43)
 Spending and Earning Money
181(12)
 Identify a polynomial expression
 Identify a polynomial function
 Add and subtract polynomial expressions
 Add and subtract polynomial functions
 Viewing the Algebra of Functions
193(5)
 Explore adding and subtracting functions graphically
 How Does Your Garden Grow?
198(10)
 Multiply two binomials using the FOIL method
 Multiply two polynomial functions
 Apply property of exponents to multiply powers having the same base
 Stargazing
208(9)
 Convert scientific notation to decimal notation
 Convert decimal notation to scientific notation
 Apply the property of exponents to divide powers having the same base
 Apply the property of exponents a0 = 1, where a ≠ 0
 Apply the property of exponents a-n = 1/an, where a ≠ 0, and n is any real number
 What Have I Learned?
217(1)
 How Can I Practice
218(6)
 Composition and Inverse of Functions
224(59)
 Inflated Balloons
224(6)
 Determine the composition of two functions
 Explore the relationship between f(g(x)) and g(f(x))
 Finding a Bargain
230(5)
 Solve problems using the composition of functions
 The Square of a Cube
235(9)
 Objectives: Apply the property of exponents to simplify an expression involving a power to a power
 Apply the property of exponents to expand the power of a product
 Determine the nth root of a real number
 Write a radical as a power having a rational exponent and as a rational exponent having a power
 Study Time
244(7)
 Determine the inverse of a function represented by a table of values
 Use the notation f-1 to represent an inverse function
 Use the property f(f-1(x)) = f-1(f(x)) = x to recognize inverse functions
 Determine the domain and range of a function and its inverse
 Temperature Conversions
251(11)
 Determine the equation of the inverse of a function represented by an equation
 Describe the relationship between the graphs of inverse functions
 Determine the graph of the inverse of a function represented by a graph
 Use the graphing calculator to produce graphs of an inverse function
 What Have I Learned?
262(2)
 How Can I Practice?
264(7)
 Chapter 2 Summary
271(4)
 Chapter 2 Gateway Review
275(8)
 Exponential and Logarithmic Functions
283(128)
 Exponential Functions
283(62)
 The Summer Job
283(14)
 Determine the growth or decay factor of an exponential function
 Identify the properties of the graph of an exponential function defined by y = bx, where b > 0 and b ≠ 1
 Graph an exponential function
 Cellular Phones
297(11)
 Determine the growth and decay factor for an exponential function represented by a table of values or an equation
 Graph exponential functions defined by y = abx, where b > 0 and b ≠ 1
 Determine the doubling and halving time
 Population Growth
308(8)
 Determine annual growth or decay rate of an exponential function represented by a table of values or an equation
 Graph an exponential function having equation y = a(1 + r)x
 Photocopying Machines
316(3)
 Generate data given the growth or decay rate of an exponential function
 Write exponential functions given the growth or decay rate
 Graph exponential functions from data
 Determine doubling and halving times from exponential functions
 Compound Interest
319(12)
 Apply the compound interest and continuous compounding formulas to a given situation
 Graph base e exponential functions
 Solve problems involving continuous growth and decay models
331(6)
 Determine the equation of an exponential function that best fits the given data
 Make predictions using an exponential regression equation
 Determine whether a linear or exponential model best fits the data
 What Have I Learned?
337(1)
 How Can I Practice?
338(7)
 Logarithmic Functions
345(66)
 The Diameter of Spheres
345(9)
 Define logarithm
 Write an exponential statement in logarithmic form
 Write a logarithmic statement in exponential form
 Determine log and In using the calculator
 Walking Speed of Pedestrians
354(7)
 Determine the inverse of the exponential function
 Identify properties of the graph of y = log x
 Identify the properties of the graph of a logarithmic function
 Graph the natural logarithmic function
 Walking Speed of Pedestrians, continued
361(9)
 Compare the average rate of change of increasing logarithmic, linear, and exponential functions
 Determine the regression equation of a natural logarithmic function that best fits a set of data
 The Elastic Ball
370(11)
 Apply the log of a product property
 Apply the log of a quotient property
 Apply the log of a power property
 Discover change of base formula
 Prison Growth
381(7)
 Solve exponential equations both graphically and algebraically
 Frequency and Pitch
388(4)
 Solve logarithmic equations both graphically and algebraically
 What Have I Learned?
392(2)
 How Can I Practice
394(5)
 Chapter 3 Summary
399(4)
 Chapter 3 Gateway Review
403(8)
 Quadratic and Higher-Order Polynomial Functions
411(118)
 Introduction to Quadratic Functions
411(60)
 Baseball and the Sears Tower
411(10)
 Objectives: Identify functions of the form f(x) = ax2 + bx + c as quadratic functions
 Explore the role of a as it relates to the graph of f(x) = ax2 + bx + c
 Explore the role of b as it relates to the graph of f(x) = ax2 + bx + c
 Explore the role of c as it relates to the graph of f(x) = ax2 + bx + c
 The Shot Put
421(13)
 Determine the vertex or turning point of a parabola
 Determine the axis of symmetry of a parabola
 Identify the domain and range
 Determine the vertical intercept of a parabola
 Determine the horizontal-intercept(s) of a parabola graphically
 Per Capita Personal Income
434(7)
 Solve quadratic equations numerically
 Solve quadratic equations graphically
 Solve quadratic inequalities graphically
 Sir Isaac Newton
441(7)
 Factor expressions by removing the greatest common factor
 Factor trinomials using trial and error
 Use the zero-product principle to solve equations
 Solve quadratic equations by factoring
 Motorcycle Deaths
448(9)
 Solve quadratic equations by the quadratic formula
 Air Quality in Atlanta
457(6)
 Determine quadratic regression models using the graphing calculator
 Solve problems using quadratic regression models
 What Have I Learned?
463(2)
 How Can I Practice?
465(6)
 Complex Numbers and Problem Solving Using Quadratic Functions
471(18)
 Complex Numbers
471(8)
 Identify the imaginary unit i = √-1
 Identify a complex number
 Determine the value of the discriminant b2 - 4ac
 Determine the types of solutions to a quadratic equation
 Solve a quadratic equation in the complex number system
 Airfare
479(4)
 Build a quadratic model as a product of linear models
 Analyze a model contextually
 Chemical-Waste Holding Region
483(2)
 Solving problems using quadratic functions
 What Have I Learned?
485(1)
 How Can I Practice?
486(3)
 Curve Fitting and Higher Order Polynomial Functions
489(40)
 The Power of Power Functions
489(8)
 Identify a direct variation function
 Determine the constant of variation
 Identify the properties of graphs of power functions defined by y = kxn, where n is a positive integer, k ≠ 0
 Hot Air Balloon
497(7)
 Identify equations that define polynomial functions
 Determine the degree of a polynomial function
 Determine the intercepts of the graph of a polynomial function
 Identify the properties of the graphs of polynomial functions
 Stolen Bases
504(6)
 Determine the regression equation of a polynomial function that best fits the data
 Distinguish between a discrete function and a continuous function
 Finding the Maximum Volume
510(2)
 Problem solving using polynomial functions
 What Have I Learned?
512(2)
 How Can I Practice
514(5)
 Chapter 4 Summary
519(4)
 Chapter 4 Gateway Review
523(6)
 Rational and Radical Functions
529(116)
 Rational Functions
529(68)
 Speed Limits
529(10)
 Determine the domain and range of a function defined by y = k/x, k is a nonzero real number
 Determine the vertical and horizontal asymptotes of the graph of y = k/x
 Sketch a graph of functions of the form y = k/x
 Determine the properties of graphs having equation y = k/x
 Loudness of a Sound
539(13)
 Graph an inverse variation function defined by an equation of the form y = k/xn, where n is any positive integer
 Describe the properties of graphs having equation y = k/x01>Determine the constant of proportionality (also called the constant of variation)
 Percent Markup
552(10)
 Determine the domain of a rational function defined by an equation of the form y = k/g(x), where k is a nonzero constant and g(x) is a polynomial expression
 Identify the vertical and horizontal asymptotes of y = k/g(x)
 Sketch a graph of rational functions defined by y = k/g(x)
 Blood-Alcohol Levels
562(14)
 Solve an equation involving a rational expression using an algebraic approach
 Solve an equation involving a rational expression using a graphing approach
 Determine horizontal asymptotes of the graph of y = f(x)/g(x), where f(x) and g(x) are first-degree polynomials
 Traffic Flow
576(8)
 Determine the least common denominator (LCD) of two or more rational expressions
 Solve an equation involving rational expressions using an algebraic approach
 Solve a formula for a specific variable
 Electrical Circuits
584(6)
 Add and subtract rational expressions
 Simplify a complex fraction
 What Have I Learned?
590(1)
 How Can I Practice?
591(6)
597(48)
 Hang Time
597(14)
 Determine the domain of a radical function defined by where g(x) is a polynomial
 Graph functions having equation y = √g(x) and y = √g(x)
 Identify the properties of the graph of y = √g(x) and y = √g(x)
 Falling Objects
611(10)
 Solve an equation involving a radical expression using a graphical and algebraic approach
 Propane Tank
621(9)
 Determine the domain of a function defined by an equation of the form y = n√g(x), where n is a positive integer and g(x) is a polynomial
 Graph y = n√g(x)
 Identify the properties of graphs of y = n√g(x)
 Solve radical equations that contain radical expressions with an index other than 2
 What Have I Learned?
630(1)
 How Can I Practice?
631(2)
 Chapter 5 Summary
633(4)
 Chapter 5 Gateway Review
637(8)
 Introduction to the Trigonometric Functions
645(1)
 Introducing the Sine, Cosine, and Tangent Functions
645(41)
 The Leaning Tower of Pisa
645(10)
 Identify the sides and corresponding angles of a right triangle
 Determine the length of the sides of similar right triangles using proportions
 Determine the sine, cosine, and tangent of an angle using a right triangle
 Determine the sine, cosine, and tangent of an acute angle by using the graphing calculator
 A Gasoline Problem
655(6)
 Identify complementary angles
 Demonstrate that the sine and cosine of complementary angles are equal
 The Sidewalks of New York
661(6)
 Determine the inverse tangent of a number
 Determine the inverse sine and cosine of a number using the graphing calculator
 Identify the domain and range of the inverse sine, cosine, and tangent functions
 Solving a Murder
667(5)
 Determine the measure of all sides and all angles of a right triangle
 How Stable Is That Tower?
672(4)
 Solve problems using right-triangle trigonometry
 Seeing Abraham Lincoln
676(4)
 Solve optimization problems using right-triangle trigonometry and by analyzing graphs
 What Have I Learned?
680(3)
 How Can I Practice?
683(3)
 Why Are the Trigonometric Functions Called Circular Functions?
686(1)
 Learn Trig or Crash!
686(11)
 Determine the coordinates of points on a unit circle using sine and cosine functions
 Sketch a graph of y = sin x and y = cos
 Identify the properties of the graphs of the sine and cosine functions
 It Won't Hertz
697(7)
 Convert between degree and radian measure
 Identify the period and frequency of a function defined by y = a sin (bx) or y = a cos(bx) using the graph
 Get in Shape
704(6)
 Determine the amplitude of the graph of y = a sin (bx) or y = a cos (bx)
 Speeding Up
710(5)
 Determine the period of the graph of y = a sin (bx) and y = a cos (bx) using a formula
 Running with a Friend
715(5)
 Determine the displacement of y = a sin (bx + c) and y = a cos(bx + c) using a formula
 What Have I Learned?
720(1)
 How Can I Practice?
721(4)
 Chapter 6 Summary
725(4)
 Chapter 6 Gateway Review
729
 APPENDIXES
 Appendix A Concept Review
1(22)
 Appendix B Trigonometry
23(10)
 Appendix C The TI-83 Plus Graphing Calculator
33(14)