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Description
- Overview:
- (Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)
En calificaciones anteriores, los estudiantes definen, evalúan y comparan las funciones y las usan para modelar las relaciones entre las cantidades. En este módulo, los estudiantes extienden su estudio de funciones para incluir la notación de la función y los conceptos de dominio y rango. Exploran muchos ejemplos de funciones y sus gráficos, centrándose en el contraste entre las funciones lineales y exponenciales. Interpretan funciones dadas gráfica, numérica, simbólica y verbalmente; traducir entre representaciones; y comprender las limitaciones de varias representaciones.
Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.
English Description:
In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
- Subject:
- Algebra
- Level:
- High School
- Material Type:
- Module
- Provider:
- New York State Education Department
- Provider Set:
- EngageNY
- Date Added:
- 09/17/2013
- License:
-
Creative Commons Attribution Non-Commercial Share Alike
- Language:
- Spanish
- Media Format:
- Text/HTML
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Standards
Learning Domain: Algebra: Creating Equations
Standard: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Algebra: Reasoning with Equations and Inequalities
Standard: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Algebra: Seeing Structure in Expressions
Standard: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Building Functions
Standard: Write a function that describes a relationship between two quantities.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Building Functions
Standard: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n 䊫 1 (n is greater than or equal to 1).
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Interpreting Functions
Standard: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Linear, Quadratic, and Exponential Models
Standard: Distinguish between situations that can be modeled with linear functions and with exponential functions.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Linear, Quadratic, and Exponential Models
Standard: Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Linear, Quadratic, and Exponential Models
Standard: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Linear, Quadratic, and Exponential Models
Standard: Interpret the parameters in a linear or exponential function in terms of a context.*
Degree of Alignment: Not Rated (0 users)
Cluster: Write expressions in equivalent forms to solve problems
Standard: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Degree of Alignment: Not Rated (0 users)
Cluster: Create equations that describe numbers or relationship
Standard: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*
Degree of Alignment: Not Rated (0 users)
Cluster: Represent and solve equations and inequalities graphically
Standard: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*
Degree of Alignment: Not Rated (0 users)
Cluster: Understand the concept of a function and use function notation.
Standard: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Degree of Alignment: Not Rated (0 users)
Cluster: Understand the concept of a function and use function notation.
Standard: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Degree of Alignment: Not Rated (0 users)
Cluster: Understand the concept of a function and use function notation.
Standard: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1 (n is greater than or equal to 1).
Degree of Alignment: Not Rated (0 users)
Cluster: Interpret functions that arise in applications in terms of the context
Standard: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
Degree of Alignment: Not Rated (0 users)
Cluster: Interpret functions that arise in applications in terms of the context
Standard: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*
Degree of Alignment: Not Rated (0 users)
Cluster: Interpret functions that arise in applications in terms of the context
Standard: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*
Degree of Alignment: Not Rated (0 users)
Cluster: Analyze functions using different representations
Standard: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
Degree of Alignment: Not Rated (0 users)
Cluster: Analyze functions using different representations
Standard: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Degree of Alignment: Not Rated (0 users)
Cluster: Build a function that models a relationship between two quantities
Standard: Write a function that describes a relationship between two quantities.*
Degree of Alignment: Not Rated (0 users)
Cluster: Build new functions from existing functions
Standard: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Degree of Alignment: Not Rated (0 users)
Cluster: Construct and compare linear, quadratic, and exponential models and solve problems
Standard: Distinguish between situations that can be modeled with linear functions and with exponential functions.*
Degree of Alignment: Not Rated (0 users)
Cluster: Construct and compare linear, quadratic, and exponential models and solve problems
Standard: Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).*
Degree of Alignment: Not Rated (0 users)
Cluster: Construct and compare linear, quadratic, and exponential models and solve problems
Standard: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.*
Degree of Alignment: Not Rated (0 users)
Cluster: Interpret expressions for functions in terms of the situation they model
Standard: Interpret the parameters in a linear or exponential function in terms of a context.*
Degree of Alignment: Not Rated (0 users)
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