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Which set of points does not represent a one-to-one function?

{(9,8),(8,9),(5,6),(6,4),(1,7)}

{(9,6),(0,4),(3,5),(1,9),(5,6)}

{(1,5),(4,0),(8,2),(3,1),(7,8)}

{(2,7),(5,4),(4,0),(1,5),(3,2)}

Which set of points does not represent a one-to-one function?\newline{(9,8),(8,9),(5,6),(6,4),(1,7)} \{(9,8),(8,9),(5,6),(6,4),(1,7)\} \newline{(9,6),(0,4),(3,5),(1,9),(5,6)} \{(9,6),(0,4),(3,5),(1,9),(5,6)\} \newline{(1,5),(4,0),(8,2),(3,1),(7,8)} \{(1,5),(4,0),(8,2),(3,1),(7,8)\} \newline{(2,7),(5,4),(4,0),(1,5),(3,2)} \{(2,7),(5,4),(4,0),(1,5),(3,2)\}

Full solution

Q. Which set of points does not represent a one-to-one function?\newline{(9,8),(8,9),(5,6),(6,4),(1,7)} \{(9,8),(8,9),(5,6),(6,4),(1,7)\} \newline{(9,6),(0,4),(3,5),(1,9),(5,6)} \{(9,6),(0,4),(3,5),(1,9),(5,6)\} \newline{(1,5),(4,0),(8,2),(3,1),(7,8)} \{(1,5),(4,0),(8,2),(3,1),(7,8)\} \newline{(2,7),(5,4),(4,0),(1,5),(3,2)} \{(2,7),(5,4),(4,0),(1,5),(3,2)\}
  1. Function Definition: A one-to-one function, also known as an injective function, is a function where each xx-value is paired with exactly one unique yy-value, and no yy-value is repeated. To determine which set of points does not represent a one-to-one function, we need to check if any yy-value is repeated for different xx-values in each set.
  2. Check First Set: Check the first set of points: (9,8),(8,9),(5,6),(6,4),(1,7){(9,8),(8,9),(5,6),(6,4),(1,7)}. We see that all yy-values are unique for different xx-values. Therefore, this set represents a one-to-one function.
  3. Check Second Set: Check the second set of points: (9,6),(0,4),(3,5),(1,9),(5,6){(9,6),(0,4),(3,5),(1,9),(5,6)}. We see that the yy-value 66 is repeated for xx-values 99 and 55. Therefore, this set does not represent a one-to-one function.
  4. Conclusion: Since we have already found a set that does not represent a one-to-one function, we can conclude the problem. However, for completeness, let's check the remaining sets.
  5. Check Third Set: Check the third set of points: (1,5),(4,0),(8,2),(3,1),(7,8){(1,5),(4,0),(8,2),(3,1),(7,8)}. We see that all yy-values are unique for different xx-values. Therefore, this set represents a one-to-one function.
  6. Check Fourth Set: Check the fourth set of points: (2,7),(5,4),(4,0),(1,5),(3,2){(2,7),(5,4),(4,0),(1,5),(3,2)}. We see that all yy-values are unique for different xx-values. Therefore, this set represents a one-to-one function.

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