Spotting Functions in Tables and Mapping Diagrams
Spotting Functions in Tables and Mapping Diagrams is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 6: Functions. Students learn to identify whether a relation is a function by checking that every input has exactly one output in tables and mapping diagrams. Multiple inputs sharing the same output is allowed, but a single input cannot have multiple different outputs.
Key Concepts
Property Relations can be represented in three equivalent forms: ordered pairs (x, y), tables, and mapping diagrams with arrows.
To be a function, every input must have exactly one arrow pointing away from it (in a diagram) or correspond to exactly one output (in a table). It is completely acceptable for different inputs to share the same output.
Examples Valid Function: A table shows the months of the year (input) and the number of days in that month (output). Multiple months like January and March have the exact same output (31 days), which is perfectly allowed.
Common Questions
How do you determine if a table represents a function?
Check the input column for repeated values. If any input value appears more than once with different output values, it is not a function. If every input maps to exactly one output, it is a function.
How do you tell if a mapping diagram is a function?
Every input must have exactly one arrow pointing to an output. If any input has two or more arrows pointing to different outputs, it is not a function.
Can two different inputs have the same output in a function?
Yes. Multiple inputs can share the same output and the relation is still a function. For example, both January and March can have 31 days as output.
Give an example of a relation that is NOT a function.
A mapping diagram where input -1 has arrows pointing to both 5 and 7. Since -1 maps to two different outputs, this violates the function definition.