Identifying Functions from Relations Using Tables and Mapping Diagrams
Identifying functions from relations using tables and mapping diagrams is a Grade 9 Algebra 1 skill in California Reveal Math (Unit 2: Relations and Functions). A relation is a function if and only if each input (domain element) maps to exactly one output. In a mapping diagram, each domain value must have only one outgoing arrow. In a table, no x-value may appear with two different y-values. For example, x=4 mapped to both y=2 and y=6 in a table means the relation is NOT a function.
Key Concepts
A relation is any set of ordered pairs $(x, y)$. A relation is a function if and only if each input value (domain element) is paired with exactly one output value (range element). If any input maps to more than one output, the relation is not a function.
Mapping Diagram Test: Draw arrows from each domain value to its range value(s). If any domain value has more than one arrow leaving it, the relation is not a function.
Common Questions
What makes a relation a function?
A relation is a function if and only if each input value in the domain maps to exactly one output value. No domain element can have two or more different outputs.
How do you use a table to determine if a relation is a function?
Check if any x-value appears more than once with different y-values. If x=4 appears with y=2 and y=6, the relation is not a function. Every x-value must be unique or always map to the same y.
How do you use a mapping diagram to test for a function?
Draw arrows from each domain value to its range value. If any domain element has more than one arrow leaving it, the relation is not a function. Multiple inputs mapping to the same output is allowed.
Can two different inputs map to the same output in a function?
Yes. For domain {-1, 0, 2} mapping to range {5, 5, 3}: both -1 and 0 map to 5, but each input has exactly one arrow. This IS a function because no input has two different outputs.
What are the domain and range of a relation?
The domain is the set of all input values (x-values). The range is the set of all output values (y-values). For the table with x = 1, 2, 3 and y = 3, 5, 7: domain = {1, 2, 3} and range = {3, 5, 7}.