#### PC.1: Students use polynomial, rational, and algebraic functions to write functions and draw graphs to solve word problems, to find composite and inverse functions, and to analyze functions and graphs. They analyze and graph circles, ellipses, parabolas, and hyperbolas.

PC.1.1: Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators.

PC.1.2: Find domain, range, intercepts, zeros, asymptotes, and points of discontinuity of functions. Use paper and pencil methods and graphing calculators.

PC.1.3: Model and solve word problems using functions and equations.

PC.1.4: Define, find, and check inverse functions.

PC.1.7: Apply transformations to functions.

PC.1.10: Write the equations of conic sections in standard form (completing the square and using translations as necessary), in order to find the type of conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.).

#### PC.2: Students solve word problems involving logarithmic and exponential functions. They draw and analyze graphs and find inverse functions.

PC.2.2: Find the domain, range, intercepts, and asymptotes of logarithmic and exponential functions.

PC.2.3: Draw and analyze graphs of logarithmic and exponential functions.

PC.2.4: Define, find, and check inverse functions of logarithmic and exponential functions.

#### PC.4: Students define trigonometric functions using the unit circle and use degrees and radians. They draw and analyze graphs, find inverse functions, and solve word problems.

PC.4.1: Define sine and cosine using the unit circle.

PC.4.2: Convert between degree and radian measures.

PC.4.4: Solve word problems involving applications of trigonometric functions.

PC.4.5: Define and graph trigonometric functions (i.e., sine, cosine, tangent, cosecant, secant, cotangent).

PC.4.6: Find domain, range, intercepts, periods, amplitudes, and asymptotes of trigonometric functions.

PC.4.8: Define and graph inverse trigonometric functions.

PC.4.9: Find values of trigonometric and inverse trigonometric functions.

PC.4.11: Make connections between right triangle ratios, trigonometric functions, and circular functions.

#### PC.5: Students prove trigonometric identities, solve trigonometric equations, and solve word problems.

PC.5.2: Use basic trigonometric identities to verify other identities and simplify expressions.

PC.5.3: Understand and use the addition formulas for sines, cosines, and tangents.

#### PC.6: Students define polar coordinates and complex numbers and understand their connection with trigonometric functions.

PC.6.4: Define complex numbers, convert complex numbers to trigonometric form, and multiply complex numbers in trigonometric form.

#### PC.7: Students define and use arithmetic and geometric sequences and series, understand the concept of a limit, and solve word problems.

PC.7.4: Use recursion to describe a sequence.

#### PC.8: Students model data with linear and nonlinear functions.

PC.8.1: Find linear models using the median fit and least squares regression methods. Decide which model gives a better fit.

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

PC.8.3: Find a quadratic, exponential, logarithmic, power, or sinusoidal function to model a data set and explain the parameters of the model.

#### PC.9: Mathematical Reasoning and Problem Solving

PC.9.4: Use the properties of number systems and order of operations to justify the steps of simplifying functions and solving equations.

PC.9.5: Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation, and that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that similar logic applies to solving systems of equations simultaneously.

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.