Unit 1: Functions Definition of a function Multiple representations of functions Determine the domain of function algebraically, graphically, and implicitly in application problems Analyze graphs to determine domain, range, relative and absolute extrema, intervals of increasing, decreasing, and constant behavior, intercepts, zeros, end behavior, evaluate, intervals where f(x) > 0 and f(x) < 0 Determine whether a function is odd or even algebraically Transformations of graphs of parent functions – horizontal and vertical translations, reflections over the x- and y-axes, horizontal and vertical stretches or shrinks Create new functions through combinations and compositions Define inverse relations and functions and determine whether an inverse relation is a function by showing one-to-one Determine the inverse of a one-to-one function graphically, numerically, and algebraically Verify/proof that two functions are inverses using compositions

Unit 2: Polynomial Functions Use the degree and leading coefficient of a polynomial to determine end behavior, maximum number of turns, number of zeros, and maximum possible x-intercepts Determine a zero’s multiplicity and understand the effects on the graph Long division and synthetic division of polynomial functions Apply the Remainder and Factor Theorem and make connections between remainders and factors Apply the Rational Zero Test to fully factor a polynomial function and determine all zeros Use Descartes’ Rule of Signs, and upper and lower bounds to make decisions for appropriate use of the Rational Zero Test Write a possible polynomial function given its graph or characteristics of the function Write a possible algebraic representation of a function given its zero, including complex Solve and graph polynomial inequalities

Unit 3: Rational Functions Determine the domain of a rational function Determine the difference between removable and non-removable discontinuities Define asymptotes and determine the equations for horizontal, vertical, and slant and other asymptotes (extension) Use asymptotes, removable discontinuities, intercepts, and additional points to graph rational functions Write a possible rational function given a graph or verbal description of characteristics Solve rational equations Solve and graph rational inequalities

Unit 4: Exponential and Logarithmic Functions Simplify expressions containing rational exponents Graph and identify transformations of exponential functions, including the number e Use exponential models and solve real-world problems Define logarithm and use the definition to convert between logarithmic and exponential forms Use properties of logarithms to simplify and evaluate expressions Determine the domain and range of an exponential and a logarithmic function Graph logarithmic functions using its inverse function relationship and transformations Define and graph natural logarithmic functions Apply the Change of Base Formula to rewrite logarithms Apply the Product, Quotient, and Power Rules to expand and condense logarithmic expressions Solve exponential and logarithmic equations, including those with substitution and extraneous solutions Use given exponential and logarithmic models to solve real-world problems

Unit 5: Unit Circle Trigonometry Define angles in degrees and radians Sketch angles in standard position Identify coterminal, reference, complementary, and supplementary angles, and quadrantal angles Convert between radian and degree measure Develop the unit circle Define and evaluate the six trigonometric functions on and off the unit circle Understand the periodic nature of the functions and use the period to evaluate coterminal angles Derive and apply Reciprocal, Quotient, and Pythagorean Identities

Unit 6: Graphing Trigonometric Functions Graph the parent sine and cosine curves based on the unit circle Identify and sketch the principle period, amplitude, and phase shift of y = sin x and y = cos x Use transformations of the sine and cosine curves to graph transformations Graph secant and cosecant functions using transformations of sine and cosine functions and the reciprocal relationship Identify the domain of the six trigonometric functions and use the period to describe any asymptotes Write a possible trigonometric function for a graph or given application Classify the six trigonometric functions as odd or even Graph the basic tangent and cotangent functions Write a possible trigonometric function for a graph or given application Use transformations to the tangent and cotangent functions to graph transformations Determine domain and range of inverse trigonometric functions Evaluating inverse trigonometric functions Evaluating compositions of trigonometric functions and their inverses

Unit 7: Trigonometric Equations and Identities Use identities (Reciprocal, Quotient, Pythagorean, Cofunction, and Even/Odd Identities) to evaluate and simplify trigonometric expressions Prove trigonometric identities Solve trigonometric equations algebraically Develop Sum and Difference Formulas and use them to evaluate and simplify expressions, solve equations, and prove identities Derive and use Double and Half-Angle Formulas to evaluate and simplify expressions, solve equations, and prove identities Solve triangles using Law of Sines, including the ambiguous case Solve triangles using Law of Cosines Use Heron’s Formula to find the area of a triangle