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Which set of points represents a function which is not one-to-one?
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Q. Which set of points represents a function which is not one-to-one?
- Definition of One-to-One Function: A function is one-to-one if each -value maps to a unique -value, meaning no two different -values map to the same -value. To determine which set of points represents a function that is not one-to-one, we need to check if there is any repetition in the -values for different -values.
- Set Analysis: Let's examine the first set of points: We need to check if any -value is repeated for different -values.Looking at the -values: , we see that they are all unique.This set represents a one-to-one function.
- Set Analysis: Now let's examine the second set of points: We need to check if any -value is repeated for different -values. Looking at the -values: , , , , , we see that they are all unique. However, we notice that the -value is repeated with different -values ( and ), which is not allowed in a function. Therefore, this set does not represent a function at all, let alone a one-to-one function.
- Set Analysis: Next, let's examine the third set of points: We need to check if any -value is repeated for different -values. Looking at the -values: , we see that the -value is repeated for different -values ( and ). This set represents a function that is not one-to-one.
- Set Analysis: Finally, let's examine the fourth set of points: We need to check if any -value is repeated for different -values.Looking at the -values: , we see that they are all unique.This set represents a one-to-one function.
