Determine whether each relation defines a function. See Example 1. {(9,-2),(-3,5),(9,1)}

Verified step by step guidance

1. Identify the definition of a function: A relation is a function if each input (or domain value) is associated with exactly one output (or range value).
2. List the input values (x-coordinates) from the given relation: {9, -3, 9}.
3. Check for any repeated input values: Notice that the input value '9' appears more than once.
4. Examine the outputs (y-coordinates) for the repeated input: The input '9' is associated with two different outputs, '-2' and '1'.
5. Conclude whether the relation is a function: Since the input '9' corresponds to more than one output, the relation does not define a function.

Key Concepts

Function Definition

A function is a specific type of relation where each input (or 'x' value) is associated with exactly one output (or 'y' value). This means that for any given value of 'x', there cannot be two different corresponding 'y' values. Understanding this definition is crucial for determining whether a relation qualifies as a function.

Ordered Pairs

Relations are often represented as sets of ordered pairs, where each pair consists of an input and an output. In the context of the question, the ordered pairs are {(9,-2),(-3,5),(9,1)}. Analyzing these pairs helps to identify if any input is repeated with different outputs, which would indicate that the relation is not a function.

Vertical Line Test

The vertical line test is a visual method used to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, the relation is not a function. While this test applies to graphical representations, it reinforces the concept that each input must map to a single output, which is essential for evaluating the given relation.