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)}
Q. 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)}
Definition of One-to-One Function: A function is one-to-one if each x-value maps to a unique y-value, meaning no two different x-values map to the same y-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 y-values for different x-values.
Set 1 Analysis: Let's examine the first set of points: (0,2),(8,8),(7,0),(1,4),(4,5)We need to check if any y-value is repeated for different x-values.Looking at the y-values: 2,8,0,4,5, we see that they are all unique.This set represents a one-to-one function.
Set 2 Analysis: Now let's examine the second set of points: {(0,2),(6,4),(1,8),(4,0),(6,7)} We need to check if any y-value is repeated for different x-values. Looking at the y-values: 2, 4, 8, 0, 7, we see that they are all unique. However, we notice that the x-value y0 is repeated with different y-values (4 and 7), 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 3 Analysis: Next, let's examine the third set of points: (1,8),(5,1),(4,8),(6,3),(3,8) We need to check if any y-value is repeated for different x-values. Looking at the y-values: 8,1,8,3,8, we see that the y-value 8 is repeated for different x-values (1,4, and 3). This set represents a function that is not one-to-one.
Set 4 Analysis: Finally, let's examine the fourth set of points: (6,6),(2,9),(3,8),(0,3),(5,2)We need to check if any y-value is repeated for different x-values.Looking at the y-values: 6,9,8,3,2, we see that they are all unique.This set represents a one-to-one function.