Essential Knowledge and Skills (TEKS)
111.35.P.1: The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise-defined functions.
111.35.P.1.A: describe parent functions symbolically and graphically, including f(x) = x to the n power, f(x) = 1n x, f(x) = loga x, f(x) = 1/x, f(x) = e to the x power, f(x) = |x|, f(x) = a to the x power, f(x) = sin x, f(x) = arcsin x, etc.;
111.35.P.1.B: determine the domain and range of functions using graphs, tables, and symbols;
111.35.P.1.D: recognize and use connections among significant values of a function (zeros, maximum values, minimum values, etc.), points on the graph of a function, and the symbolic representation of a function; and
111.35.P.1.E: investigate the concepts of continuity, end behavior, asymptotes, and limits and connect these characteristics to functions represented graphically and numerically.
111.35.P.2: The student interprets the meaning of the symbolic representations of functions and operations on functions to solve meaningful problems.
111.35.P.2.A: apply basic transformations, including a ? f(x), f(x) + d, f(x - c), f(b ? x), and compositions with absolute value functions, including |f(x)|, and f(|x|), to the parent functions;
111.35.P.2.B: perform operations including composition on functions, find inverses, and describe these procedures and results verbally, numerically, symbolically, and graphically; and
111.35.P.2.C: investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties.
111.35.P.3: The student uses functions and their properties, tools and technology, to model and solve meaningful problems.
111.35.P.3.A: investigate properties of trigonometric and polynomial functions;
111.35.P.3.B: use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data;
111.35.P.3.D: use properties of functions to analyze and solve problems and make predictions; and
111.35.P.3.E: solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas and incorporate radian measure where needed.
111.35.P.4: The student uses sequences and series as well as tools and technology to represent, analyze, and solve real-life problems.
111.35.P.4.A: represent patterns using arithmetic and geometric sequences and series;
111.35.P.4.B: use arithmetic, geometric, and other sequences and series to solve real-life problems;
111.35.P.4.D: apply sequences and series to solve problems including sums and binomial expansion.
111.35.P.5: The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations.
111.35.P.5.A: use conic sections to model motion, such as the graph of velocity vs. position of a pendulum and motions of planets;
Correlation last revised: 1/20/2017