1: Manipulating Functions Evaluate composite functions Evaluate composite Find composite Functions Shift Functions Transforming Functions functions: graphs and tables Model with function Model with composite Evaluate inverse functions Find inverses functions Verify inverse functions combination functions Determine if a function is Restrict domains of functions invertible to make them invertible 2: Polynomial Expressions, equations, and functions Expand binomials Prove polynomial identities Factor polynomials: complex Solve quadratic equations: Find zeros of polynomials numbers complex solutions Zeros of polynomials & their Positive and negative End behavior of polynomials Even & odd functions Even & odd polynomials graphs intervals of polynomials 3: Radical Equations and functions Solve square-root equations Solve square-root equations Extraneous solutions of Radical functions & their (basic) radical equations graph 4: Rational Expressions, equations, and functions Simplify rational expressions: Simplify rational expressions: Simplify rational expressions Multiply and divide rational Multiply and divide rational common monomial factors common binomial factors (advanced) expressions (basic) expressions Multiply and divide rational Add and subtract rational Add and subtract rational Least common multiple Add and subtract rational expressions (advanced) expressions: like expressions: unlike expressions: factored denominators denominators denominators Add and subtract rational Nested Fractions Equations with one rational Equations with one rational Equations with two rational expressions expression expression (advanced) expressions Recognized direct and End behavior of rational Rational function points of Analyze vertical asymptotes Graphs of rational functions inverse variation functions discontinuity of rational functions 5: Exponential and Logarithmic Functions Evaluate logarithms Evaluate logarithms Relationship between Use the properties of Evaluate logarithms: change (advanced) exponentials and logarithms logarithms of base rule Use the logarithm change of Solve exponential equations Solve exponential equations Exponential model word Graphs of exponential base rule using logarithms (base-10 using logarithms (base-2 and problems functions and base-e) other bases) Graphs of logarithmic functions 6: Trigonometric Functions
1: Manipulating Functions Evaluate composite functions Evaluate composite functions: graphs and tables Find composite Functions Shift Functions Transforming Functions Model with function combination Model with composite functions Evaluate inverse functions Find inverses functions Verify inverse functions Determine if a function is invertible Restrict domains of functions to make them invertible 2: Polynomial Expressions, equations, and functions Expand binomials Prove polynomial identities Factor polynomials: complex numbers Solve quadratic equations: complex solutions Find zeros of polynomials Zeros of polynomials & their graphs Positive and negative intervals of polynomials End behavior of polynomials Even & odd functions Even & odd polynomials 3: Radical Equations and functions Solve square-root equations (basic) Solve square-root equations Extraneous solutions of radical equations Radical functions & their graph 4: Rational Expressions, equations, and functions Simplify rational expressions: common monomial factors Simplify rational expressions: common binomial factors Simplify rational expressions (advanced) Multiply and divide rational expressions (basic) Multiply and divide rational expressions Multiply and divide rational expressions (advanced) Add and subtract rational expressions: like denominators Add and subtract rational expressions: unlike denominators Least common multiple Add and subtract rational expressions: factored denominators Add and subtract rational expressions Nested Fractions Equations with one rational expression Equations with one rational expression (advanced) Equations with two rational expressions Recognized direct and inverse variation End behavior of rational functions Rational function points of discontinuity Analyze vertical asymptotes of rational functions Graphs of rational functions 5: Exponential and Logarithmic Functions Evaluate logarithms Evaluate logarithms (advanced) Relationship between exponentials and logarithms Use the properties of logarithms Evaluate logarithms: change of base rule Use the logarithm change of base rule Solve exponential equations using logarithms (base-10 and base-e) Solve exponential equations using logarithms (base-2 and other bases) Exponential model word problems Graphs of exponential functions Graphs of logarithmic functions 6: Trigonometric Functions