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Intermediate Algebra by Trigsted, Gallaher, and Bodden is the first online, completely "clickable" Intermediate Algebra text to take full advantage of MyMathLab's features and benefits. Kirk Trigsted saw marked improvements in student learning when he started teaching with MyMathLab, but he noticed that most students started their assignments by going directly to the MyMathLab homework exercises without consulting their textbook. This inspired Kirk to write a true eText, built within MyMathLab, to create a dynamic, seamless learning experience that would better meet the needs and expectations of his students. Completely clickable and fully integrated-the Trigsted eText is designed for today's learners. Intermediate Algebra is also available with two printed resources to provide additional support for your classroom:The Summary Notebook is a spiral-bound, printed version of the eText that provides a place for students to do practice work and summarize key concepts from the online videos and animations. In addition to the benefits it provides students, the Summary Notebook also provides portability for those instructors that prefer a printed text for class preparation. The Guided Notebook is an interactive workbook that guides students through the course by asking them to write down key definitions and work through important examples for each section of the eText. This resource is available in a three-hole-punched, unbound format to provide the foundation for a personalized course notebook. Students can integrate their class notes and homework notes within the appropriate section of the Guided Notebook. Instructors can customize the Guided Notebook files found within MyMathLab. This package contains the MyMathLab Student Access Kit plus the Summary Notebook.
Contents
Chapter R. ReviewR.1 Sets of Numbers1 Identify sets2 Classify real numbers3 Plot real numbers on a number line4 Use inequality symbols to order real numbers5 Compute the absolute value of a real numberR.2 Order of Operations and Properties of Real Numbers1 Perform operations on real numbers2 Simplify numeric expressions containing exponents and radicals3 Identify and use the properties of real numbers4 Use order of operations to evaluate numeric expressionsR.3 Algebraic Expressions1 Evaluate algebraic expressions2 Simplify algebraic expressions3 Write verbal descriptions as algebraic expressionsChapter 1. Equations and Inequalities in One Variable1.1 Linear Equations in One Variable1 Determine if a given value is a solution to an equation2 Solve linear equations in one variable3 Identify equations that are contradictions and those that are identities4 Use linear equations to solve application problems1.2 Linear Inequalities in One Variable1 Determine if a given value is a solution to an inequality2 Graph the solution set of an inequality on a number line3 Use interval notation to express the solution set of an inequality4 Solve linear inequalities in one variable5 Use linear inequalities to solve application problems1.3 Compound Inequalities; Absolute Value Equations and Inequalities1 Find the union and intersection of two sets2 Solve compound linear inequalities in one variable3 Solve absolute value equations4 Solve absolute value inequalities1.4 Formulas and Problem Solving1 Solve a formula for a given variable2 Use formulas to solve application problemsChapter 2. Graphs and Functions2.1 The Rectangular Coordinate System and Graphing1 Plot ordered pairs in the rectangular coordinate system2 Determine if an ordered pair is a solution to an equation3 Find unknown coordinates4 Graph equations by plotting points5 Find x- and y-intercepts2.2 Relations and Functions1 Identify independent and dependent variables2 Find the domain and range of a relation3 Determine if relations are functions4 Determine if graphs are functions5 Solve application problems involving relations and functions2.3. Function Notation and Applications1 Express equations of functions using function notation2 Evaluate functions3 Graph simple functions by plotting points4 Interpret graphs of functions5 Solve application problems involving functions2.4 Graphs of Linear Functions1 Graph linear functions by plotting points2 Graph linear functions by using intercepts3 Graph vertical and horizontal lines2.5 Linear Equations in Two Variables1 Find the slope of a line2 Graph a line using the slope and a point3 Determine the relationship between two lines4 Write the equation of a line from given information5 Write equations of parallel and perpendicular lines6 Use linear models to solve application problems; direct variation2.6 Linear Inequalities in Two Variables1 Determine if an ordered pair is a solution to a linear inequality in two variables2 Graph a linear inequality in two variablesChapter 3. Systems of Linear Equations and Inequalities3.1 Systems of Linear Equations in Two Variables1 Determine if an ordered pair is a solution to a system of linear equations in two variables2 Solve systems of linear equations in two variables by graphing3 Solve systems of linear equations in two variables by substitution4 Solve systems of linear equations in two variables by elimination5 Solve inconsistent and dependent systems6 Use systems of linear equations in two variables to solve application problems3.2 Systems of Linear Equations in Three Variables1 Determine if an ordered triple is a solution to a system of linear equations in three variables2 Solve systems of linear equations in three variables3 Use systems of linear equations in three variables to solve application problems3.3 More Problem Solving with Systems of Linear Equations1 Use systems of linear equations to solve uniform motion problems2 Use systems of linear equations to solve geometry problems3 Use systems of linear equations to solve mixture problems3.4 Systems of Linear Inequalities in Two Variables1 Determine if an ordered pair is a solution to a system of linear inequalities in two variables2 Graph systems of linear inequalities in two variablesChapter 4. Polynomial Expressions and Functions4.1 Rules for Exponents1 Simplify exponential expressions using the product rule2 Simplify exponential expressions using the quotient rule3 Use the zero-power rule4 Use the negative-power rule5 Use the power-to-power rule6 Use the product-to-power and quotient-to-power rules7 Simplify exponential expressions using a combination of rules8 Use rules for exponents with scientific notation4.2 Introduction to Polynomial Functions1 Find the coefficient and degree of a monomial2 Find the leading coefficient and degree of a polynomial3 Evaluate a polynomial function for a given value4 Add polynomials5 Subtract polynomials6 Add and subtract polynomial functions4.3 Multiplying Polynomials1 Multiply monomials2 Multiply a polynomial by a monomial3 Multiply two binomials4 Multiply two binomials using special product rules5 Multiply two or more polynomials6 Multiply polynomial functions4.4 Dividing Polynomials1 Divide a polynomial by a monomial2 Divide polynomials using long division3 Divide polynomials using synthetic division4 Divide polynomial functions5 Use the Remainder and Factor theoremsChapter 5. Factoring5.1 Greatest Common Factor and Factoring by Grouping1 Factor out the greatest common factor from a polynomial2 Factor by grouping5.2 Factoring Trinomials1 Factor trinomials of the form x2 + bx + c 2 Factor trinomials of the form ax2 + bx + c using trial-and-error3 Factor trinomials of the form ax2 + bx + c using the ac method4 Factor trinomials using substitution5.3 Special-Case Factoring; A General Factoring Strategy1 Factor the difference of two squares2 Factor perfect square trinomials3 Factor the sum or difference of two cubes4 Factor polynomials completely5.4 Polynomial Equations and Models1 Solve polynomial equations by factoring2 Find the zeros of a polynomial function3 Use polynomial equations and models to solve application problemsChapter 6. Rational Expressions, Equations, and Functions6.1 Introduction to Rational Expressions and Functions1 Find the domain of a rational function2 Evaluate rational functions3 Simplify rational expressions6.2 Multiplying and Dividing Rational Expressions1 Multiply rational expressions2 Divide rational expressions6.3 Adding and Subtracting Rational Expressions1 Add and subtract rational expressions with common denominators2 Find the least common denominator of rational expressions3 Add and subtract rational expressions with unlike denominators6.4 Complex Rational Expressions1 Simplify complex rational expressions by first simplifying the numerator and denominator 2 Simplify complex rational expressions by multiplying by a common denominator6.5 Rational Equations and Models1 Identify rational equations2 Solve rational equations3 Find the zeros of a rational function4 Use rational equations to solve application problems6.6 Variation1 Solve application problems involving direct variation2 Solve application problems involving inverse variation2 Solve application problems involving combined variationChapter 7. Radicals and Rational Exponents7.1 Radical Expressions1 Find square roots of perfect squares2 Approximate square roots3 Simplify radical expressions of the form v(a2)4 Find cube roots5 Find and approximate nth roots7.2 Radical Functions1 Evaluate radical functions2 Find the domain of a radical function3 Graph functions that contain square roots or cube roots7.3 Rational Exponents and Simplifying Radical Expressions1 Use the definition for rational exponents of the form a1/n2 Use the definition for rational exponents of the form am/n3. Simplify exponential expressions involving rational exponents4 Use rational exponents to simplify radical expressions5 Simplify radical expressions using the product rule6 Simplify radical expressions using the quotient rule7.4 Operations with Radicals1 Add and subtract radical expressions2 Multiply radical expressions3 Rationalize denominators of radical expressions7.5 Radical Equations and Models1 Solve equations involving one radical expression2 Solve equations involving two radical expressions3 Use radical equations and models to solve application problems7.6 Complex Numbers1 Simplify powers of i2 Add and subtract complex numbers3 Multiply complex numbers4 Divide complex numbers5 Simplify radicals with negative radicands Chapter 8. Quadratic Equations and Functions; Circles8.1 Solving Quadratic Equations1 Solve quadratic equations using factoring2 Solve quadratic equations using the square root property3 Solve quadratic equations by completing the square4 Solve quadratic equations using the quadratic formula5 Use the discriminant to determine the number and type of solutions to a quadratic equation6 Solve equations that are quadratic in form8.2 Quadratic Functions and Their Graphs1 Identify the characteristics of a quadratic function from its graph2 Graph quadratic functions by using translations3 Graph quadratic functions of the form f(x) = a(x-h)2 + k 4 Find the vertex of a parabola by completing the square5 Graph quadratic functions of the form f(x) = ax2 + bx + c by completing the square6 Find the vertex of a parabola by using the vertex formula7 Graph quadratic functions of the form f(x) = ax2 + bx + c by using the vertex formula8.3 Applications and Modeling of Quadratic Functions1 Solve applications involving unknown numbers2 Solve applications involving projectile motion3 Solve applications involving geometric formulas4 Solve applications involving distance, rate, and time5 Solve applications involving work6 Maximize quadratic functions to solve application problems7 Minimize quadratic functions to solve application problems8.4 Circles1 Find the distance between two points2 Find the midpoint of a line segment3 Write the standard form of an equation of a circle4 Sketch the graph of a circle5 Find the center and radius of a circle8.5 Polynomial and Rational Inequalities1 Solve polynomial inequalities2 Solve rational inequalitiesChapter 9. Exponential and Logarithmic Functions and Equations9.1 Transformations of Functions1 Use vertical shifts to graph functions2 Use horizontal shifts to graph functions3 Use reflections to graph functions4 Use vertical stretches and compressions to graph functions5 Use horizontal stretches and compressions to graph functions6 Use a combination of transformations to graph functions9.2 Composite and Inverse Functions1 Form and evaluate composite functions2 Determine the domain of composite functions3 Determine if a function is one-to-one using the horizontal line test4 Verify inverse functions5 Sketch the graphs of inverse functions6 Find the inverse of a one-to-one function9.3 Exponential Functions1 Use the characteristics of exponential functions2 Sketch the graph of exponential functions using transformations3 Solve exponential equations by relating the bases4 Solve applications of exponential functions9.4 The Natural Exponential Function1 Use the characteristics of the natural exponential function2 Sketch the graph of natural exponential functions using transformations3 Solve natural exponential equations by relating the bases4 Solve applications of natural exponential functions9.5 Logarithmic Functions1 Use the definition of a logarithmic function2 Evaluate logarithmic expressions3 Use the properties of logarithms4 Use the common and natural logarithms5 Use the characteristics of logarithmic functions6 Sketch the graph of logarithmic functions using transformations7 Find the domain of logarithmic functions9.6 Properties of Logarithms1 Use the product rule, quotient rule, and power rule for logarithms2 Expand and condense logarithmic expressions3 Solve logarithmic equations by using the logarithm property of equality4 Use the change-of-base formula9.7 Exponential and Logarithmic Equations1 Solve exponential equations2 Solve logarithmic equations9.8 Applications of Exponential and Logarithmic Functions1 Solve compound interest applications2 Solve exponential growth and decay applications3 Solve logistic growth applications4 Use Newton's Law of CoolingAppendix A. Conic SectionsIntroduction to Conic SectionsA.1 The Parabola1 Work With the Equation of a Parabola with a Vertical Axis of Symmetry2 Work With the Equation of a Parabola with a Horizontal Axis of Symmetry3 Find the Equation of a Parabola Given Information about the Graph4 Complete the Square to Find the Equation of a Parabola in Standard Form5 Solve Applications Involving ParabolasA.2 The Ellipse1 Sketch the Graph of an Ellipse2 Find the Equation of an Ellipse Given Information about the Graph3 Complete the Square to Find the Equation of an Ellipse in Standard Form4 Solve Applications Involving EllipsesA.3 The Hyperbola1 Sketch the Graph of a Hyperbola2 Find the Equation of a Hyperbola in Standard Form3 Complete the Square to Find the Equation of a Hyperbola in Standard Form4 Solve Applications Involving HyperbolasAppendix B Sequences and SeriesB.1 Introduction to Sequences and Series1 Write the terms of a sequence2 Write the terms of a recursive sequence3 Write the general term for a given sequence4 Compute partial sums of a series5 Determine the sum of a finite series written in summation notation6 Write a series using summation notationB.2 Arithmetic Sequences and Series1 Determine if a sequence is arithmetic2 Find the general term or specific term of an arithmetic sequence3 Compute the nth partial sum of an arithmetic series4 Solve applications of arithmetic sequences and seriesB.3 Geometric Sequences and Series1 Write the terms of a geometric sequence2 Determine if a sequence is geometric2 Find the general term or specific term of a geometric sequence3 Compute the nth partial sum of a geometric series5 Determine if an infinite geometric series converges or diverges4 Solve applications of geometric sequences and seriesB.4 The Binomial Theorem1 Expand binomials raised to a power using Pascal's Triangle2 Evaluate binomial coefficients3 Expand binomials raised to a power using the Binomial Theorem4 Find a particular term or a particular coefficient of a binomial expansionAppendix C Basic Math Review - Fractions, Decimals, Proportions, PercentsC.1 FractionsC.2 DecimalsC.3 ProportionsC.4 Percents
