Preface 

xiii  


1  (180) 


1  (42) 


1  (12) 

Distinguish between input and output 





Represent a function numerically and graphically 



Write a function using function notation 




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 




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 




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 




36  (1) 


37  (6) 


43  (53) 


43  (8) 

Determine the average rate of change 




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 




63  (10) 

Determine the slopeintercept form of a line given the slope and vertical intercept 



Determine the slopeintercept form of a line given two points on the line 



Compare the slopes of parallel lines 




73  (9) 

Write an equation of a line in general form Ax + By = C 



Write the slopeintercept form of a linear equation given the general form 




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 




88  (2) 


90  (6) 

Systems of Linear Equations, Inequalities, and Absolute Value Functions 


96  (85) 


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 




109  (7) 

Solve a 2 X 2 linear system algebraically using the substitution method and the addition method 



Solve equations containing parentheses 




116  (5) 

Solve a 3 X 3 linear system of equations 




121  (13) 

Solve linear inequalities numerically and graphically 



Use properties of inequalities to solve linear inequalities algebraically 



Solve compound inequalities algebraically and graphically 




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 





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 




156  (2) 


158  (5) 


163  (6) 


169  (12) 


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 




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 an = 1/an, where a ≠ 0, and n is any real number 




217  (1) 


218  (6) 

Composition and Inverse of Functions 


224  (59) 


224  (6) 

Determine the composition of two functions 



Explore the relationship between f(g(x)) and g(f(x)) 




230  (5) 

Solve problems using the composition of functions 




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 




244  (7) 

Determine the inverse of a function represented by a table of values 



Use the notation f1 to represent an inverse function 



Use the property f(f1(x)) = f1(f(x)) = x to recognize inverse functions 



Determine the domain and range of a function and its inverse 




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 




262  (2) 


264  (7) 


271  (4) 


275  (8) 

Exponential and Logarithmic Functions 


283  (128) 


283  (62) 


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 




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 




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 




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 




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 




337  (1) 


338  (7) 


345  (66) 


345  (9) 



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 




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 




381  (7) 

Solve exponential equations both graphically and algebraically 




388  (4) 

Solve logarithmic equations both graphically and algebraically 




392  (2) 


394  (5) 


399  (4) 


403  (8) 

Quadratic and HigherOrder 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 




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 horizontalintercept(s) of a parabola graphically 



Per Capita Personal Income 


434  (7) 

Solve quadratic equations numerically 



Solve quadratic equations graphically 



Solve quadratic inequalities graphically 




441  (7) 

Factor expressions by removing the greatest common factor 



Factor trinomials using trial and error 



Use the zeroproduct principle to solve equations 



Solve quadratic equations by factoring 




448  (9) 

Solve quadratic equations by the quadratic formula 




457  (6) 

Determine quadratic regression models using the graphing calculator 



Solve problems using quadratic regression models 




463  (2) 


465  (6) 

Complex Numbers and Problem Solving Using Quadratic Functions 


471  (18) 


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 




479  (4) 

Build a quadratic model as a product of linear models 



Analyze a model contextually 



ChemicalWaste Holding Region 


483  (2) 

Solving problems using quadratic functions 




485  (1) 


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 




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 




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 




512  (2) 


514  (5) 


519  (4) 


523  (6) 

Rational and Radical Functions 


529  (116) 


529  (68) 


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 




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) 




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) 




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 firstdegree polynomials 




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 




584  (6) 

Add and subtract rational expressions 



Simplify a complex fraction 




590  (1) 


591  (6) 


597  (48) 


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) 




611  (10) 

Solve an equation involving a radical expression using a graphical and algebraic approach 




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 





Identify the properties of graphs of y = n√g(x) 



Solve radical equations that contain radical expressions with an index other than 2 




630  (1) 


631  (2) 


633  (4) 


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 




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 




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 righttriangle trigonometry 




676  (4) 

Solve optimization problems using righttriangle trigonometry and by analyzing graphs 




680  (3) 


683  (3) 

Why Are the Trigonometric Functions Called Circular Functions? 


686  (1) 


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 




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 




704  (6) 

Determine the amplitude of the graph of y = a sin (bx) or y = a cos (bx) 




710  (5) 

Determine the period of the graph of y = a sin (bx) and y = a cos (bx) using a formula 




715  (5) 

Determine the displacement of y = a sin (bx + c) and y = a cos(bx + c) using a formula 




720  (1) 


721  (4) 


725  (4) 


729  



Appendix A Concept Review 


1  (22) 


23  (10) 

Appendix C The TI83 Plus Graphing Calculator 


33  (14) 
Selected Answers 

47  (24) 
Glossary 

71  (4) 
Index 

75  