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M3-020-A09-V03
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F-BF.4.a
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M3-020-A09-V03
Find inverse functions for simple invertible functions, including rational examples.
Decide one-to-one status from fixed evidence
Problem
A function table has distinct inputs \(1\) and \(3\) that both output \(5\). Use this evidence to determine one-to-one status, the table-test result, and whether the inverse relation is a function.
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A
Evidence: inputs 1 and 3 both have output 5. Conclusion: the relation is one-to-one, the table test passes, and its inverse relation is a function because inverse input 5 has one output.
B
Evidence: inputs 1 and 3 both have output 5. Conclusion: the relation is not one-to-one, the table test fails, and its inverse relation is not a function because inverse input 5 would have two outputs.
C
Evidence: output 8 occurs only once. Conclusion: the relation is one-to-one, the table test passes, and its inverse relation is a function without checking the repeated output 5.
D
Evidence: the three input values are distinct. Conclusion: the relation is one-to-one, the table test passes, and its inverse relation is a function even though output 5 repeats.
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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
