Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Transcribed Image Text:**Question:**
Which of the following relations does not represent a function?
**Options:**
A. \(\{(4, 4), (5, 4), (6, 4)\}\)
B. \(\{(4, 4), (4, 5), (4, 6)\}\)
C. \(\{(4, 5), (5, 5), (6, 5)\}\)
D. \(\{(4, 4), (5, 5), (6, 6)\}\)
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**Explanation:**
A relation is considered a function if each element of the domain (the set of all first components) is paired with exactly one element of the range (the set of all second components).
- **Option A**: Each element of the domain (4, 5, 6) is paired with one unique element of the range (all 4). This is a function.
- **Option B**: The element 4 in the domain is paired with multiple elements in the range (4, 5, 6). This does not represent a function because one domain element corresponds to multiple range elements.
- **Option C**: Each element of the domain (4, 5, 6) is paired with one unique element of the range (all 5). This is a function.
- **Option D**: Each element of the domain (4, 5, 6) is paired with one unique element of the range (4, 5, 6). This is a function.
**Conclusion:**
The correct answer is **B**. This relation does not represent a function since the element 4 in the domain corresponds to more than one element in the range.
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