(c)  Knowledge and skills.

(1)  The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, radical, exponential, logarithmic, trigonometric, and piecewise-defined functions. The student is expected to:

(A)  describe parent functions symbolically and graphically, including y = xⁿ, y = ln x, y = log_a x, y = , y = e^x, y = a^x, y = sin x, etc.;
(B)  determine the domain and range of functions using graphs, tables, and symbols;
(C)  describe symmetry of graphs of even and odd functions;
(D)  recognize and use connections among significant points of a function (roots, maximum points, and minimum points), the graph of a function, and the symbolic representation of a function; and
(E)  investigate continuity, end behavior, vertical and horizontal asymptotes, and limits and connect these characteristics to the graph of a function.

(2)  The student interprets the meaning of the symbolic representations of functions and operations on functions within a context. The student is expected to:

(A)  apply basic transformations, including a • f(x), f(x) + d, f(x - c), f(b • x), |f(x)|, f(|x|), to the parent functions;
(B)  perform operations including composition on functions, find inverses, and describe these procedures and results verbally, numerically, symbolically, and graphically; and
(C)  investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties.

(3)  The student uses functions and their properties to model and solve real-life problems. The student is expected to:

(A)  use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data;
(B)  use regression to determine a function to model real-life data;
(C)  use properties of functions to analyze and solve problems and make predictions; and
(D)  solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas.

(4)  The student uses sequences and series to represent, analyze, and solve real-life problems. The student is expected to:

(A)  represent patterns using arithmetic and geometric sequences and series;
(B)  use arithmetic, geometric, and other sequences and series to solve real-life problems;
(C)  describe limits of sequences and apply their properties to investigate convergent and divergent series; and
(D)  apply sequences and series to solve problems including sums and binomial expansion.

(5)  The student uses conic sections, their properties, and parametric representations to model physical situations. The student is expected to:

(A)  use conic sections to model motion, such as the graph of velocity vs. position of a pendulum and motions of planets;
(B)  use properties of conic sections to describe physical phenomena such as the reflective properties of light and sound;
(C)  convert between parametric and rectangular forms of functions and equations to graph them; and
(D)  use parametric functions to simulate problems involving motion.

(6)  The student uses vectors to model physical situations. The student is expected to:

(A)  use the concept of vectors to model situations defined by magnitude and direction; and
(B)  analyze and solve vector problems generated by real-life situations.