Determine whether each relation defines a function. See Example 1.

Verified step by step guidance

1. insert step 1> Identify the given relation, which is typically a set of ordered pairs or a graph.
2. insert step 2> Recall the definition of a function: A relation is a function if each input (x-value) is associated with exactly one output (y-value).
3. insert step 3> Examine the relation: For each x-value, check if there is only one corresponding y-value.
4. insert step 4> If any x-value is paired with more than one y-value, the relation is not a function.
5. insert step 5> If every x-value is paired with exactly one y-value, then the relation is a function.

Key Concepts

Function Definition

A function is a specific type of relation where each input (or domain element) is associated with exactly one output (or range element). This means that for every x-value in the domain, there must be a unique y-value in the range. Understanding this definition is crucial for determining if a given relation qualifies as a function.

Vertical Line Test

The vertical line test is a visual method used to determine if a relation is a function. If any vertical line drawn on the graph of the relation intersects the graph at more than one point, the relation is not a function. This test provides a straightforward way to assess the uniqueness of outputs for given inputs.

Ordered Pairs

Relations can be represented as sets of ordered pairs, where each pair consists of an input and its corresponding output. To determine if a relation is a function, one can examine these pairs to check for repeated x-values with different y-values. If any x-value appears with multiple y-values, the relation does not define a function.