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.2.1: 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.3.1: 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.4.1: 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.5.1: 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.6.1: 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.7.1: Define vectors as objects having magnitude and direction. Represent vectors geometrically.
PC.7.5: Model and solve problems using parametric equations.
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