Math Problem Statement
Which set of ordered pairs represents a function?
Solution
To determine which set of ordered pairs represents a function, we need to ensure that each input (or "x" value) is associated with only one output (or "y" value). In other words, no x-value should repeat with different y-values.
Let’s analyze each option:
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Set 1:
- The x-value is paired with two different y-values: and .
- This set does not represent a function.
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Set 2:
- The x-value is paired with two different y-values: and .
- This set does not represent a function.
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Set 3:
- The x-value is paired with two different y-values: and .
- This set does not represent a function.
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Set 4:
- Each x-value is unique and has only one corresponding y-value.
- This set does represent a function.
Answer: The correct answer is Set 4: .
Would you like a detailed explanation on why a function requires unique x-values?
Here are some related questions to practice:
- How can you identify a function from a graph?
- What is the "vertical line test" for functions?
- What happens when multiple x-values share the same y-value? Is it still a function?
- How can functions be represented using tables, mappings, or graphs?
- What is the difference between one-to-one functions and regular functions?
Tip: Remember, in a function, each input (x) must be associated with exactly one output (y).
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Math Problem Analysis
Mathematical Concepts
Functions
Ordered Pairs
Formulas
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Theorems
Definition of a Function
Suitable Grade Level
Grades 8-10