State the domain and range for each relation. Then determine whether each relation represents a

step 1 Here in this question, we've been given a relation and that is represented by a mapping. So one

State the domain and range for each relation. Then determine...

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Key Concepts

Domain

The domain of a relation or function is the set of all possible input values (often represented as x-values) that can be used in the relation. This concept is essential for understanding which inputs can be fed into the mapping from one set to another.

Range

The range is the set of all possible output values (often represented as y-values) that result from applying the relation or function to the domain. It highlights the variety of outputs that can occur based on the given inputs.

Relation

A relation in mathematics is a collection of ordered pairs that shows how elements from one set are paired with elements from another set. It generalizes the concept of a function by not necessarily requiring a unique output for each input.

Function

A function is a particular type of relation where each input (from the domain) is associated with exactly one output (in the range). This one-to-one or well-defined correspondence ensures that functions behave predictably and are fundamental to many mathematical processes.

Vertical Line Test

The vertical line test is a graphical criterion used to determine whether a relation is a function. If no vertical line intersects the graph of the relation at more than one point, the relation qualifies as a function.

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