#### PC.1: Relations and Functions

PC.1.1: Use paper and pencil methods and technology to graph polynomial, absolute value, rational, algebraic, exponential, logarithmic, trigonometric, inverse trigonometric and piecewise-defined functions. Use these graphs to solve problems, and translate among verbal, tabular, graphical and symbolic representations of functions by using technology as appropriate.

PC.1.2: Identify domain, range, intercepts, zeros, asymptotes and points of discontinuity of functions represented symbolically or graphically, using technology as appropriate.

PC.1.3: Solve word problems that can be modeled using functions and equations.

PC.1.4: Recognize and describe continuity, end behavior, asymptotes, symmetry and limits and connect these concepts to graphs of functions.

PC.1.5: Find, interpret and graph the sum, difference, product and quotient (when it exists) of two functions and indicate the relevant domain and range of the resulting function.

PC.1.6: Find the composition of two functions and determine the domain and the range of the composite function. Conversely, when given a function, find two other functions for which the composition is the given one.

PC.1.7: Define and find inverse functions, their domains and their ranges. Verify symbolically and graphically whether two given functions are inverses of each other.

PC.1.8: Apply transformations to functions and interpret the results of these transformations verbally, graphically and numerically.

#### PC.2: Conics

PC.2.1: Derive equations for conic sections and use the equations that have been found.

PC.2.2: Graph conic sections with axes of symmetry parallel to the coordinate axes by hand, by completing the square, and find the foci, center, asymptotes, eccentricity, axes and vertices (as appropriate).

#### PC.3: Logarithmic and Exponential Functions

PC.3.1: Compare and contrast symbolically and graphically y = e to the x power with other exponential functions.

PC.3.2: Define the logarithmic function g(x) = log base a of x as the inverse of the exponential function f(x) = a to the x power. Apply the inverse relationship between exponential and logarithmic functions and the laws of logarithms to solve problems.

PC.3.3: Analyze, describe and sketch graphs of logarithmic and exponential functions by examining intercepts, zeros, domain and range, and asymptotic and end behavior.

PC.3.4: Solve problems that can be modeled using logarithmic and exponential functions. Interpret the solutions and determine whether the solutions are reasonable.

#### PC.4: Trigonometry

PC.4.1: Define and use the trigonometric ratios cotangent, secant and cosecant in terms of angles of right triangles.

PC.4.2: Model and solve problems involving triangles using trigonometric ratios.

PC.4.4: Define sine and cosine using the unit circle.

PC.4.6: Deduce geometrically and use the value of the sine, cosine and tangent functions at 0, pi/6, pi/4, pi/3 and pi/2 radians and their multiples.

PC.4.7: Make connections among right triangle ratios, trigonometric functions and the coordinate function on the unit circle.

PC.4.8: Analyze and graph trigonometric functions, including the translation of these trigonometric functions. Describe their characteristics (i.e., spread, amplitude, zeros, symmetry, phase, shift, vertical shift, frequency).

PC.4.9: Define, analyze and graph inverse trigonometric functions and find the values of inverse trigonometric functions.

PC.4.10: Solve problems that can be modeled using trigonometric functions, interpret the solutions and determine whether the solutions are reasonable.

PC.4.11: Derive the fundamental Pythagorean trigonometric identities; sum and difference identities; half-angle and double-angle identities; and the secant, cosecant and cotangent functions. Use these identities to verify other identities and simplify trigonometric expressions.

PC.4.12: Solve trigonometric equations and interpret solutions graphically.

#### PC.5: Polar Coordinates and Complex Numbers

PC.5.1: Define and use polar coordinates and relate polar coordinates to Cartesian coordinates.

PC.5.2: Represent equations given in Cartesian coordinates in terms of polar coordinates.

PC.5.3: Graph equations in the polar coordinate plane.

PC.5.4: Define complex numbers, convert complex numbers to polar form and multiply complex numbers in polar form.

PC.5.5: Prove and use De Moivre's Theorem.

#### PC.6: Sequences and Series

PC.6.1: Define arithmetic and geometric sequences and series.

PC.6.2: Derive and use formulas for finding the general term for arithmetic and geometric sequences.

PC.6.3: Develop, prove and use sum formulas for arithmetic series and for finite and infinite geometric series.

PC.6.4: Generate a sequence using recursion.

PC.6.5: Describe the concept of the limit of a sequence and a limit of a function. Decide whether simple sequences converge or diverge. Recognize an infinite series as the limit of a sequence of partial sums.

PC.6.6: Model and solve word problems involving applications of sequences and series, interpret the solutions and determine whether the solutions are reasonable.

PC.6.7: Derive the binomial theorem by combinatorics.

#### PC.7: Vectors and Parametric Equations

PC.7.1: Define vectors as objects having magnitude and direction. Represent vectors geometrically.

PC.7.5: Model and solve problems using parametric equations.

#### PC.8: Data Analysis

PC.8.1: Find linear models by using median fit and least squares regression methods. Decide which among several linear models gives a better fit. Interpret the slope in terms of the original context.

PC.8.2: Calculate and interpret the correlation coefficient. Use the correlation coefficient and residuals to evaluate a "best-fit" line.

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.