Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.
Verified step by step guidance
1
<Identify the relation: A relation is a set of ordered pairs.>
<Determine if the relation is a function: A relation is a function if each input (x-value) corresponds to exactly one output (y-value).>
<Check for repeated x-values: If any x-value is repeated with a different y-value, the relation is not a function.>
<Find the domain: The domain is the set of all possible x-values (inputs) in the relation.>
<Find the range: The range is the set of all possible y-values (outputs) in the relation.>
Recommended similar problem, with video answer:
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2m
Play a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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 one and only one corresponding y-value. Understanding this definition is crucial for determining whether a given relation qualifies as a function.
The domain of a relation is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values). Identifying the domain and range helps in understanding the behavior of the function and its limitations. It is essential to analyze the relation to accurately determine these sets.
The vertical line test is a visual method used to determine if a relation is a function. If a vertical line intersects the graph of the relation at more than one point, the relation is not a function. This test provides a quick way to assess the function property of a relation when graphed.