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Determine if the following is a function, and if it is a one-to-one function.Not a functionA function, not one-to-oneA one-to-one function
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Q. Determine if the following is a function, and if it is a one-to-one function.Not a functionA function, not one-to-oneA one-to-one function
- Check Function Criteria: To determine if the given set of ordered pairs represents a function, we need to check if each input (first component of each ordered pair) maps to exactly one output (second component of each ordered pair). We will examine the set of ordered pairs for any repeated first components with different second components.
- Unique Input-Output Mapping: Looking at the set of ordered pairs , we see that each input value is unique and maps to only one output value. Therefore, this set of ordered pairs does represent a function.
- Check One-to-One Criteria: Next, to determine if the function is one-to-one, we need to check if each output value is also unique, meaning no two different inputs map to the same output value. We will examine the set of ordered pairs for any repeated second components.
- Check One-to-One Criteria: Next, to determine if the function is one-to-one, we need to check if each output value is also unique, meaning no two different inputs map to the same output value. We will examine the set of ordered pairs for any repeated second components.Looking at the output values , we see that they are all unique. No output value is repeated, which means that no two different inputs map to the same output. Therefore, the function is one-to-one.
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