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M3-020-A09-V04
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F-BF.4.a
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M3-020-A09-V04
Find inverse functions for simple invertible functions, including rational examples.
Decide one-to-one status from fixed evidence
Problem
A table lists \((-3,~8)\), \((0,~5)\), \((2,~1)\), and \((6,~-4)\). Use the outputs to determine one-to-one status, the table-test result, and whether reversing the pairs gives a function.
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A
Evidence: the inputs −3, 0, 2, and 6 are all distinct. Conclusion: the relation is one-to-one, the table test fails, and reversing the pairs does not give a function.
B
Evidence: the outputs 8, 5, 1, and −4 are all distinct. Conclusion: the relation is not one-to-one, the table test fails, and reversing the pairs does not give a function.
C
Evidence: one output is negative while the others are positive. Conclusion: the relation is not one-to-one, the table test fails, and reversing the pairs does not give a function.
D
Evidence: the outputs 8, 5, 1, and −4 are all distinct. Conclusion: the relation is one-to-one, the table test passes, and reversing the pairs gives an inverse relation that is a function.
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Curriculum context
Standard F-BF.4.a
Category Functions
Domain Building Functions
Objective Find inverse functions for simple invertible functions, including rational examples.
Problem type Decide one-to-one status from fixed evidence
