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Основно съдържание

STANDARDS

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US-AR

Math

Arkansas Math

Advanced Topics and Modeling in Mathematics: Functions

Students will analyze and interpret functions using different representations in terms of an authentic contextual application.

F.1.ATMM.1

Fully covered
Interpret key features of graphs and tables in terms of two quantities for functions beyond the level of quadratic that model a relationship between the quantities

F.1.ATMM.2

Mostly covered
Graph functions expressed symbolically and show key features of the graph using technology

F.1.ATMM.3

Mostly covered
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions

F.1.ATMM.4

Fully covered
Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior

F.1.ATMM.5

Fully covered
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available and showing end behavior

F.1.ATMM.6

Partially covered
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude

F.1.ATMM.7

Mostly covered
Interpret the parameters of functions beyond the level of linear and quadratic in terms of a context

Students will construct and compare various types of functions and build models to represent and solve problems.

F.2.ATMM.1

Mostly covered
Model equations in two or more variables to represent relationships between quantities for functions beyond the level of linear and quadratic

F.2.ATMM.2

Mostly covered
Represent constraints or inequalities using systems of equations and/or inequalities; interpret solutions as viable or non-viable options in a modeling context for functions beyond the level of linear and quadratic

F.2.ATMM.3

Fully covered
Compose functions (e.g., If T(y) is the temperature in the atmosphere as a function of height, and h(y) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time)

F.2.ATMM.4

Fully covered
Write arithmetic and geometric sequences both recursively and with an explicit formula; use the sequences to model situations and translate between the two forms

F.2.ATMM.5

Mostly covered
Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed

F.2.ATMM.6

Fully covered
Use inverse functions to solve trigonometric equations that arise in modeling context; evaluate the solutions using technology and interpret them in terms of the context