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Questions and Answers
Which of the following correctly defines the 'domain' of a relation?
What does the range of a relation represent?
Which representation confirms that a set of ordered pairs is a function?
Under what conditions can a graph be classified as a function?
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Which of the following scenarios represents a relation rather than a function?
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Study Notes
General Mathematics Overview
- A relation is defined as a set of ordered pairs.
- The domain consists of all input values (x-values), represented as a set.
- Example: Domain = {1, 2, 3, 4}
- The range includes all output values (y-values), also represented as a set.
- Example: Range = {7, 6, 5, 4}
Functions and Their Representation
- A function is a specific type of relation where each input corresponds to exactly one output.
- Functions can be represented in various forms:
- Set of Ordered Pairs: Lists input-output pairs clearly.
-
Table of Values: Organized presentation showing inputs and their respective outputs.
- Example:
- Input: x = {1, 2, 3, 4}
- Output: f(x) = {3, 4, 5, 6}
- Example:
- Mapping Diagram: Visual representation showing how each input is mapped to an output.
- Graph: A plotted representation on a coordinate plane illustrating the relationship between x and f(x).
The Vertical Line Test
- The Vertical Line Test is a method to determine if a relation is a function:
- If any vertical line intersects the graph of the relation more than once, it is not a function.
- If every vertical line intersects the graph at most once, it confirms the relation is a function.
Distinguishing Functions from Relations
- Not all relations qualify as functions; a function has unique output for each input.
- Points and examples demonstrate both relations and functions, highlighting differences in mapping and output uniqueness.
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Description
This quiz covers fundamental concepts of relations and functions in general mathematics. You will learn about domain and range, as well as different ways to represent functions, including ordered pairs and tables. Test your understanding of how these concepts interact and form the basis for mathematical functions.
