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Which set of points represents a function which is not one-to-one?

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

{(0,2),(6,4),(1,8),(4,0),(6,7)}

{(1,8),(5,1),(4,8),(6,3),(3,8)}

{(6,6),(2,9),(3,8),(0,3),(5,2)}

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

Full solution

Q. Which set of points represents a function which is not one-to-one?\newline{(0,2),(8,8),(7,0),(1,4),(4,5)} \{(0,2),(8,8),(7,0),(1,4),(4,5)\} \newline{(0,2),(6,4),(1,8),(4,0),(6,7)} \{(0,2),(6,4),(1,8),(4,0),(6,7)\} \newline{(1,8),(5,1),(4,8),(6,3),(3,8)} \{(1,8),(5,1),(4,8),(6,3),(3,8)\} \newline{(6,6),(2,9),(3,8),(0,3),(5,2)} \{(6,6),(2,9),(3,8),(0,3),(5,2)\}
  1. Definition of One-to-One Function: A function is one-to-one if each xx-value maps to a unique yy-value, meaning no two different xx-values map to the same yy-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 yy-values for different xx-values.
  2. Set 11 Analysis: Let's examine the first set of points: (0,2),(8,8),(7,0),(1,4),(4,5){(0,2),(8,8),(7,0),(1,4),(4,5)}\newlineWe need to check if any yy-value is repeated for different xx-values.\newlineLooking at the yy-values: 2,8,0,4,52, 8, 0, 4, 5, we see that they are all unique.\newlineThis set represents a one-to-one function.
  3. Set 22 Analysis: Now let's examine the second set of points: {(0,2),(6,4),(1,8),(4,0),(6,7)}\{(0,2),(6,4),(1,8),(4,0),(6,7)\} We need to check if any yy-value is repeated for different xx-values. Looking at the yy-values: 22, 44, 88, 00, 77, we see that they are all unique. However, we notice that the xx-value yy00 is repeated with different yy-values (44 and 77), which is not allowed in a function. Therefore, this set does not represent a function at all, let alone a one-to-one function.
  4. Set 33 Analysis: Next, let's examine the third set of points: (1,8),(5,1),(4,8),(6,3),(3,8){(1,8),(5,1),(4,8),(6,3),(3,8)} We need to check if any yy-value is repeated for different xx-values. Looking at the yy-values: 8,1,8,3,88, 1, 8, 3, 8, we see that the yy-value 88 is repeated for different xx-values (1,4,1, 4, and 33). This set represents a function that is not one-to-one.
  5. Set 44 Analysis: Finally, let's examine the fourth set of points: (6,6),(2,9),(3,8),(0,3),(5,2){(6,6),(2,9),(3,8),(0,3),(5,2)}\newlineWe need to check if any yy-value is repeated for different xx-values.\newlineLooking at the yy-values: 6,9,8,3,26, 9, 8, 3, 2, we see that they are all unique.\newlineThis set represents a one-to-one function.

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