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A2-F-2-3

Page history last edited by Tashe Harris 6 years, 1 month ago

A2.F.2.3 Find and graph the inverse of a function, if it exists, in real-world and mathematical situations. Know that the domain of a function f is the range of the inverse function f-1, and the range of the function f is the domain of the inverse function f-1.


In a Nutshell

Students will find the inverse of a function algebraically, numerically, and graphically.  They will be able to interpret the inverse of a function in a real-world situation. They will understand the relationship between domains and ranges of functions and their inverses.

Student Actions

Teacher Actions

  • Students develop conceptual understanding by translating between symbolic notation and verbal representations while making mathematical and real-world connections.

  • Students will develop procedural fluency as they explore a variety of efficient procedures or algorithms for finding the inverse of a function.

 

  • Identify evidence of student progress toward understanding the relationship between the graphs of functions and their inverses.

  • Design ways to elicit and assess students’ abilities to use symbolic and verbal representations meaningfully to answer questions about functions and their inverses.

  • Identify evidence of student progress toward understanding the relationship between the domain and range of functions and their inverses, algebraically, verbally, numerically, and graphically..

  • Pose purposeful questions that provide students with opportunities to explore a variety of procedures and algorithms for finding the inverse of a function.

Key Understandings

Misconceptions

Procedural:

  • Find the inverse of a function algebraically, numerically (in a table or set of ordered pairs), or graphically.

  • Graph a function and its inverse as reflections across the line y = x.

  • Identify the range of a function, given the domain of its inverse, and vice versa.

Conceptual:

  • Give a verbal description of an inverse, within the context of a real world situation.

Procedural:

  • Students look for a graph or produce a graph that is a reflection across the y-axis or the x-axis, instead of y=x.

Conceptual:

  • Students do not realize that the domain and range of a function and its inverse are switched.

  • Students have difficulty switching the independent and dependent quantities to create a verbal description of an inverse.

OKMath Framework Introduction

Algebra 2 Grade Introduction

 


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