TEKS 111.42(c)(2)(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;
Source: Texas Administrative Code §111.42 (Chapter 111) · Adopted 2012
Knowledge & Skills 111.42(c)(2)
Functions
The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems. The student is expected to:
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Other expectations under 111.42(c)(2)
- TEKS 111.42(c)(2)(A) use the composition of two functions to model and solve real-world problems;
- TEKS 111.42(c)(2)(B) demonstrate that function composition is not always commutative;
- TEKS 111.42(c)(2)(C) represent a given function as a composite function of two or more functions;
- TEKS 111.42(c)(2)(D) describe symmetry of graphs of even and odd functions;
- TEKS 111.42(c)(2)(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;
- TEKS 111.42(c)(2)(F) graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions;
- TEKS 111.42(c)(2)(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) f…
- TEKS 111.42(c)(2)(H) graph arcsin x and arccos x and describe the limitations on the domain;
- TEKS 111.42(c)(2)(J) analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this character…
- TEKS 111.42(c)(2)(K) analyze characteristics of rational functions and the behavior of the function around the asymptotes, including horizontal, vertical, and oblique asymptotes;
- TEKS 111.42(c)(2)(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 behav…
- TEKS 111.42(c)(2)(M) describe the left-sided behavior and the right-sided behavior of the graph of a function around discontinuities;
- TEKS 111.42(c)(2)(N) analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems;
- TEKS 111.42(c)(2)(O) develop and use a sinusoidal function that models a situation in mathematical and real-world problems; and
- TEKS 111.42(c)(2)(P) determine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world problems.