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

{(1,7),(6,4),(8,0),(2,5),(4,3)}

{(9,6),(3,4),(5,8),(5,2),(1,7)}

{(7,5),(1,9),(4,2),(2,6),(6,4)}

{(5,2),(9,7),(6,6),(8,4),(0,1)}

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

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Write equations of cosine functions using properties

Full solution

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

\newline

\{(1,7),(6,4),(8,0),(2,5),(4,3)\}

\newline

\{(9,6),(3,4),(5,8),(5,2),(1,7)\}

\newline

\{(7,5),(1,9),(4,2),(2,6),(6,4)\}

\newline

\{(5,2),(9,7),(6,6),(8,4),(0,1)\}

Define One-to-One Function: Understand the definition of a one-to-one function. A one-to-one function, also known as an injective function, is a function where each $x$ -value (input) maps to a unique $y$ -value (output). This means that no two different $x$ -values can map to the same $y$ -value.
Check First Set for Repeating Y-Values: Examine the first set of points for any repeating $y$ -values. $\newline$ The first set of points is $\{(1,7),(6,4),(8,0),(2,5),(4,3)\}$ . We need to check if any $y$ -value is repeated for different $x$ -values. $\newline$ Checking the $y$ -values: $7$ , $4$ , $0$ , $5$ , $3$ - all $y$ -values are unique.
Check Second Set for Repeating Y-Values: Examine the second set of points for any repeating y-values. $\newline$ The second set of points is ${(9,6),(3,4),(5,8),(5,2),(1,7)}$ . We need to check if any y-value is repeated for different x-values. $\newline$ Checking the y-values: $6$ , $4$ , $8$ , $2$ , $7$ - all y-values are unique, but we notice that the x-value $5$ is repeated for two different y-values ( $8$ and $2$ ), which violates the definition of a one-to-one function.
Identify Non One-to-One Set: Since we have found a set that does not represent a one-to-one function, we do not need to check the remaining sets. $\newline$ We have identified that the second set of points has a repeated $x$ -value with different $y$ -values, which means it is not a one-to-one function. Therefore, we can conclude our search.

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