Is the following relation a function? Justify your answer.
Understand the Problem
The question is asking whether a specific relation meets the criteria to be classified as a function. A relation is a function if every input (or domain element) corresponds to exactly one output (or range element). To justify the answer, one would typically examine the relation and check for instances where an input is associated with more than one output.
Answer
The relation is a function if every input corresponds to exactly one output.
Answer for screen readers
The relation is a function if every input corresponds to exactly one output. If any input corresponds to multiple outputs, it is not a function.
Steps to Solve
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Identify Inputs and Outputs List all the unique inputs (domain values) and outputs (range values) in the given relation.
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Check Associations Examine how each input is paired with its corresponding output. Look for cases where an input has multiple outputs.
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Determine Function Status If every input is associated with exactly one output, then the relation is a function. If any input is associated with more than one output, then the relation is not a function.
The relation is a function if every input corresponds to exactly one output. If any input corresponds to multiple outputs, it is not a function.
More Information
This classification helps in distinguishing relations from functions in mathematics, ensuring clear input-output rules which are critical for computational processing.
Tips
- Failing to check all inputs thoroughly for multiple outputs; make sure to examine every single input.
- Assuming a relation is a function without verifying the one-to-one output condition.
