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This guide explores the criteria for determining whether a relationship is a function. It covers the vertical line test for graphs, checks for unique x-values in tables, and examines mapping diagrams where each input has one output. It also looks at equations to confirm if they fit the format y = f(x). Understanding these criteria is essential for identifying functions in various mathematical representations, ensuring clarity in mathematical communication and analysis.
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Function or Not Input Output 1 2 3 4 2 3 4 NO NO Yes Yes
Function or Not Input Output 1 2 3 4 1 2 3 4 Yes Yes Yes No
Function or Not Input Output 1 2 3 4 5 4 3 2 Yes Yes No Yes
Function or Not Input Output 5 4 3 2 Yes 1 No Yes No
Function or Not Input Output 1 2 3 4 No 2 Yes No Yes
Function or Not Input Output 2 4 6 8 1 2 3 4 Yes Yes Yes Yes
Determining Functionality • From a graph • Must pass the vertical line test (not touch in more than one place at same time) • From a table • No repeats in “X” values • From a mapping diagram • Only one arrow can come out of any one input (for ever input there is only one output) • From and equation • Is the equation written in Y=