PC.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.

PC.2.AUse the composition of two functions to model and solve real-world problems.PC.2.BDemonstrate that function composition is not always commutative.PC.2.CRepresent a given function as a composite function of two or more functions.PC.2.DDescribe symmetry of graphs of even and odd functions.PC.2.EDetermine 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.PC.2.FGraph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions.PC.2.GGraph 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.PC.2.HGraph arc sin x and arc cos x and describe the limitations on the domain.PC.2.IDetermine 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.PC.2.JAnalyze 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.PC.2.KAnalyze characteristics of rational functions and the behavior of the function around the asymptotes, including horizontal, vertical, and oblique asymptotes.PC.2.LDetermine 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;PC.2.MDescribe the left-sided behavior and the right-sided behavior of the graph of a function around discontinuities.PC.2.NAnalyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems.PC.2.ODevelop and use a sinusoidal function that models a situation in mathematical and real-world problems.PC.2.PDetermine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world problems.
Example Problems
Write an expression for a polynomial in standard form that fits this definition without adding in any extra terms:

A polynomial of the 4th degree,
using x as its only variable,
with a leading coefficient of 2,
and with no other terms
Write an expression for a polynomial in standard form that fits this definition without adding in any extra terms:

A polynomial of the 5th degree,
using x as its only variable,
with a leading coefficient of 7,
and with a constant term of 6
Write an expression for a polynomial in standard form that fits this definition without adding in any extra terms:

A polynomial of the 5th degree,
using x as its only variable,
with a leading coefficient of -5,
and with a constant term of 4
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