To determine which sets of ordered pairs represent functions based on the given definition, we need to ensure that each input (the first element of each pair) corresponds to exactly one output (the second element of each pair). Additionally, no inputs can repeat.
Let's evaluate each set of ordered pairs one by one:
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First Set:
- confused emoji, monocle emoji
- star eyed emoji, party emoji
- scared emoji, shocked emoji
- pondering emoji, jazz hands emoji
Analysis: All inputs (emojis) are unique. This set represents a function.
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Second Set:
- -2, 4
- -1, 2
- 1, 2
- 2, 4
Analysis: The input -1 corresponds to the output 2, while the input 1 also corresponds to the output 2. Since the input 1 and -1 repeat the same output, this set does not represent a function.
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Third Set:
- -3, 4
- 2, 5
- 6, 8
- -3, 2
Analysis: The input -3 corresponds to two different outputs (4 and 2). Therefore, this set does not represent a function.
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Fourth Set:
- x, y
- -2, 4
- -1, 1
- 1, 1
- 2, 4
Analysis: The input -1 corresponds to the output 1, while the input 1 also corresponds to the same output 1. Since the output for input 1 does not conflict with any other pairs, this set represents a function.
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Fifth Set:
- x, y
- -2, 4
- -1, 3
- -1, 2
- -2, 1
Analysis: The input -1 corresponds to two different outputs (3 and 2), and the input -2 also corresponds to two different outputs (4 and 1). Therefore, this set does not represent a function.
Based on this analysis, the sets that represent functions are:
- First Set
- Fourth Set
The second, third, and fifth sets do not represent functions.
1 answer