Podcast
Questions and Answers
What does the term 'domain' refer to in a relation?
What does the term 'domain' refer to in a relation?
The inverse of a relation switches the elements in each ordered pair.
The inverse of a relation switches the elements in each ordered pair.
True
What is the range of the relation \{(1, 2), (2, 3), (3, 4)\}?
What is the range of the relation \{(1, 2), (2, 3), (3, 4)\}?
\{2, 3, 4\}
The relation \{(1, 2), (2, 3), (3, 4)\} has a domain of \[blank\].
The relation \{(1, 2), (2, 3), (3, 4)\} has a domain of \[blank\].
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Which of the following pairs represents an inverse relation for the relation \{(1, 2), (2, 3), (3, 4)\}?
Which of the following pairs represents an inverse relation for the relation \{(1, 2), (2, 3), (3, 4)\}?
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The range of the inverse relation is the domain of the original relation.
The range of the inverse relation is the domain of the original relation.
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Match the following terms with their correct definitions:
Match the following terms with their correct definitions:
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What is represented by each ordered pair \(x, y\) in a relation when graphed?
What is represented by each ordered pair \(x, y\) in a relation when graphed?
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Study Notes
Relations
- A relation is a set of ordered pairs, where each pair represents a connection between an input (x-value) and an output (y-value)
- Example: The relation ({(1, 2), (2, 3), (3, 4)}) shows a specific relationship between each x-value and its corresponding y-value.
Domain and Range
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Domain: refers to all possible input values (x-values) within a relation.
- Example: In ({(1, 2), (2, 3), (3, 4)}) the domain is ({1, 2, 3}).
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Range: refers to all possible output values (y-values) within a relation.
- Example: The range of the relation ({(1, 2), (2, 3), (3, 4)}) is ({2, 3, 4}).
Graphs
- The graph of a relation is a visual representation of the ordered pairs plotted on a Cartesian plane (x-y axis).
- Each point on the graph represents an ordered pair from the relation.
- Example: The ordered pairs from ({(1, 2), (2, 3), (3, 4)}) would be plotted as points at (1, 2), (2, 3), and (3, 4).
Inverse Relations
- An inverse relation is formed by switching the x and y values within each ordered pair of the original relation.
- If the original relation is (R = {(a, b)}), the inverse relation (R^{-1} = {(b, a)}).
- Example: The inverse of (R = {(1, 2), (2, 3), (3, 4)}) is (R^{-1} = {(2, 1), (3, 2), (4, 3)}).
Domain and Range of Inverse Relations
- The domain of an inverse relation is the range of the original relation.
- Example: The range of (R = {(1, 2), (2, 3), (3, 4)}) is ({2, 3, 4}), which becomes the domain of (R^{-1}).
- The range of an inverse relation is the domain of the original relation.
- Example: The domain of (R = {(1, 2), (2, 3), (3, 4)}) is ({1, 2, 3}), which becomes the range of (R^{-1}).
Graphs of Inverse Relations
- The graph of an inverse relation can be obtained by reflecting the original relation's graph across the line (y = x).
- This means that the x and y coordinates are essentially flipped.
- Example: If the original graph of (R) has points (1, 2), (2, 3), and (3, 4), then the inverse relation (R^{-1}) will have points (2, 1), (3, 2), and (4, 3).
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Description
Test your understanding of relations, including ordered pairs, domain, and range. This quiz covers concepts such as how to identify the domain and range from a given set of ordered pairs, as well as how to graph these relations. Dive into the world of functions and inverse relations!
