Set: A well-defined collection of objects, called the elements or members of the sets. Ordered pairs: A composition of the x-coordinate (abscissa) and y-coordinate (ordinate) havin... Set: A well-defined collection of objects, called the elements or members of the sets. Ordered pairs: A composition of the x-coordinate (abscissa) and y-coordinate (ordinate) having two values written in a fixed order within the parenthesis. Relation: Just a relationship between sets of information usually presented by ordered pairs. Domain: Of a function is the set X. That is a collection for all possible x-values. Range: Of a function is the set of all images as x varies throughout the domain, a collection of all possible y-values. Function: Is a well-defined relation wherein each member of the first set or domain corresponds to exactly one element of the second set or the range. Can be represented through ordered pairs, tables, and graphical forms.
Understand the Problem
The question provides definitions for various mathematical concepts including sets, ordered pairs, relations, domain, range, and functions. It appears to serve as a reference or explanation of these key topics in mathematics.
Answer
A function is a well-defined relation where each domain element corresponds to exactly one range element.
A function is a well-defined relation where each element of the domain corresponds to exactly one element of the range.
Answer for screen readers
A function is a well-defined relation where each element of the domain corresponds to exactly one element of the range.
More Information
A function ensures that no x-value in the domain maps to more than one y-value in the range. This property is crucial for the definition of a function and distinguishes it from general relations.
Tips
A common mistake is confusing functions with general relations. Ensure each x-value maps to only one y-value.
Sources
- 2.1: Introduction to Functions - Mathematics LibreTexts - math.libretexts.org
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