A apply mathematics to problems arising in everyday life, society, and the workplace;

B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;

D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

E create and use representations to organize, record, and communicate mathematical ideas;

F analyze mathematical relationships to connect and communicate mathematical ideas; and

G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

A use the composition of two functions to model and solve real-world problems;

B demonstrate that function composition is not always commutative;

C represent a given function as a composite function of two or more functions;

D describe symmetry of graphs of even and odd functions;

E determine an inverse function, when it exists, for a given function over its domain or a subset of its domain and represent the inverse using multiple representations;

F graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions;

G graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems;

H graph arcsin x and arccos x and describe the limitations on the domain;

I determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing;

J analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems;

K analyze characteristics of rational functions and the behavior of the function around the asymptotes, including horizontal, vertical, and oblique asymptotes;

L determine various types of discontinuities in the interval (-∞, ∞) as they relate to functions and explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities;

M describe the left-sided behavior and the right-sided behavior of the graph of a function around discontinuities;

N analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems;

O develop and use a sinusoidal function that models a situation in mathematical and real-world problems; and

P determine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world problems.

A graph a set of parametric equations;

B convert parametric equations into rectangular relations and convert rectangular relations into parametric equations;

C use parametric equations to model and solve mathematical and real-world problems;

D graph points in the polar coordinate system and convert between rectangular coordinates and polar coordinates;

E graph polar equations by plotting points and using technology;

F determine the conic section formed when a plane intersects a double-napped cone;

G make connections between the locus definition of conic sections and their equations in rectangular coordinates;

H use the characteristics of an ellipse to write the equation of an ellipse with center (h, k); and

I use the characteristics of a hyperbola to write the equation of a hyperbola with center (h, k).

A determine the relationship between the unit circle and the definition of a periodic function to evaluate trigonometric functions in mathematical and real-world problems;

B describe the relationship between degree and radian measure on the unit circle;

C represent angles in radians or degrees based on the concept of rotation and find the measure of reference angles and angles in standard position;