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
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Teacher Actions
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Identify evidence of student progress toward understanding the relationship between the graphs of functions and their inverses.
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Design ways to elicit and assess students’ abilities to use symbolic and verbal representations meaningfully to answer questions about functions and their inverses.
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Identify evidence of student progress toward understanding the relationship between the domain and range of functions and their inverses, algebraically, verbally, numerically, and graphically..
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Pose purposeful questions that provide students with opportunities to explore a variety of procedures and algorithms for finding the inverse of a function.
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Key Understandings
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Misconceptions
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Procedural:
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Find the inverse of a function algebraically, numerically (in a table or set of ordered pairs), or graphically.
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Graph a function and its inverse as reflections across the line y = x.
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Identify the range of a function, given the domain of its inverse, and vice versa.
Conceptual:
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Procedural:
Conceptual:
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Students do not realize that the domain and range of a function and its inverse are switched.
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Students have difficulty switching the independent and dependent quantities to create a verbal description of an inverse.
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OKMath Framework Introduction
Algebra 2 Grade Introduction
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