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Summary of changes in Math 64 effective Fall 2014: We now start the course by introducing functions. Additionally, we cover the review of linear inequalities, using inequalities in business applications, compound inequalities, and solving absolute value inequalities as well as the absolute value equations. Exponential decay, conic sections, and solving non-linear systems of equations are added as optional topics. INTRODUCTORY AND INTERMEDIATE ALGEBRA 4TH EDITION BY ROBERT BLITZER TOPIC SECTION OBJECTIVES/NOTES STUDENTS SHOULD BE PROFICIENT IN THE SKILLS REPRESENTED BY THE FOLLOWING RANGE OF ITEMS IN THE BLITZER PROBLEM SETS Introduction 8.1 Full coverage 1-23 odd, 31, 33, 39, 43 to Functions Emphasis on function notation Find the domain and range of a relation Determine whether a relation is a function Evaluate a function Graphs of 8.2 Full coverage 1-45 Functions Use the vertical line test to identify functions Obtain information about a function from its graph Review interval notation Identify the domain and range of a function from its graph The Algebra 8.3 Full coverage 1-57 odd of Functions Find the domain of a function Use the algebra of functions to combine functions and determine domains Composite 8.4 Full coverage 1-53 odd and Inverse Form composite functions Functions Verify inverse functions Find the inverse of a function Use the horizontal line test to determine if a function has an inverse function Use the graph of a one-to-one function to graph its inverse function Reviewing 9.1 Full coverage 1-35 odd Linear Review how to solve linear inequalities Inequalities Use linear inequalities to solve problems and Using involving revenue, cost, and profit Inequalities in Business Applications Compound 9.2 Full coverage (Emphasis on “and” vs. “or” 1-57 odd Inequalities Find the intersection of two sets Solve compound inequalities involving and Find the union of two sets Solve compound inequalities involving or Equations and 9.3 Inequalities Involving Absolute Full coverage Solve absolute value equations Solve absolute value inequalities in the form 1-81 odd u c Solve absolute value inequalities in the form u c Recognize absolute value inequalities with no solution or all real numbers as solutions Full coverage/ Emphasis on function notation and domain restrictions Evaluate square roots and square root functions Find the domain of square root functions Simplify expressions of the form n a n Find even and odd roots Full coverage Radical Expressions and Functions 10.1 Rational Exponents 10.2 10.3 Adding, Subtracting, and Dividing Radical Expressions 10.4 Multiplying 10.5 With More Than One Term and Rationalizing Denominators Radical Equations Complex Numbers 10.6 10.7 1-111 odd 1 n Use the definition of a m n m Use the definition of a n Simplify expressions with rational exponents Simplify radical expressions using rational exponents Full coverage (Emphasis on function notation) Use the product rule to multiply radicals Use factoring and the product rule to simplify radicals Multiply radicals and then simplify Full coverage Add and subtract radical expressions Use the quotient rule to simplify radical expressions Use the quotient rule to divide radical expressions Full coverage Multiply radical expressions with more than one term Use polynomial special products to multiply radicals Rationalize denominators containing one term Rationalize denominators containing two terms Full coverage (Emphasis on function notation) Solve radical equations Full coverage Express square roots of negative numbers in terms of i Add and subtract complex numbers Multiplying and Simplifying Radical Expressions Use the definition of a 1-89 odd, 113 1-81 odd 1-65 odd 1-91 odd 1-37 odd 1-99 odd The Square Root Property and Completing the Square; Distance and Midpoint Formulas 11.1 The Quadratic Formula 11.2 Quadratic Functions and their Graphs 11.3 Multiply complex numbers Divide complex numbers Simplify powers of i Full coverage Solve quadratic equations using the square root property (Emphasize) Complete the square of a binomial Solve quadratic equations by completing the square Solve problems using the square root property Find the distance between two points Find the midpoint of a line segment Full coverage Solve quadratic equations using the quadratic formula (Emphasize) Use the discriminant to determine the number and type of solutions Determine the most efficient method to use when solving a quadratic equation Write quadratic equations from solutions Use the quadratic formula to solve problems Full coverage/Emphasis on the connection between vertex form and general form and connection between graphs and function notation Recognize characteristics of parabolas Graph parabolas in the form 1-91 1-57 odd, 77 1-43 odd, 57, 59, 61, 63 2 f x a x h k Graph parabolas in the form f x ax 2 bx c Determine a quadratic function's minimum or maximum value Solve problems involving a quadratic function's minimum or maximum value Full coverage Solve equations that are quadratic in form Equations Quadratic in Form Exponential Functions 11.4 Logarithmic Functions 12.2 12.1 Full coverage Evaluate exponential functions Graph exponential functions Evaluate functions with base e Use compound interest formulas Full coverage (Emphasize the link between exponential and logarithmic form) Change from logarithmic to exponential form Change from exponential to logarithmic form Evaluate logarithms Use basic logarithm properties Graph logarithmic functions 1-37 1-47 odd 1-71 odd Properties of Logarithms 12.3 Exponential and Logarithmic Equations 12.4 Exponential Growth and Decay 12.5 The Circle 13.1 Systems of 13.5 Nonlinear Equations in Two Variables Find the domain of a logarithmic function Use common logarithms Use natural logarithms Full coverage Use the product rule Use the quotient rule Use the power rule Expand logarithmic expressions Condense logarithmic expressions Use the change-of-base property Full coverage (Emphasize that a logarithm is an exponent) Use like bases to solve exponential equations Use logarithms to solve exponential equations Use exponential form to solve logarithmic equations Use the one-to-one property of logarithms to solve logarithmic equations Solve applied problems involving exponential and logarithmic equations Full coverage Model Exponential Growth and Decay Choose an appropriate Model for Data Full coverage Write the standard form of a circle’s equation Give the center and radius of a circle whose equation is in standard form Convert the general form of a circle’s equation to standard form (use completing the square) Emphasize systems that include linear and quadratic equations, and equations of circles. Recognize systems of nonlinear equations in two variables Solve systems of nonlinear equations by substitution Solve systems of nonlinear equations by addition 1-67 odd, 75-85 odd, 80 (answer is false) 1-89 odd, 99, 111 1-31 odd 1-25 odd 1-8, 11-12, 17-18, 25-28, 30, 3537, 39-42