Questions: Question 8 Which xy-pair in the relation shown in the table below causes the relation to not be a function? (In other words, which xy-pair could be removed to make the relation into a function) x-values y-values 1 6 1 -6 2 9 3 9 4 12 (2,9) (3,9) (4,12) (1,6)

Question 8 Which xy-pair in the relation shown in the table below causes the relation to not be a function? (In other words, which xy-pair could be removed to make the relation into a function) x-values y-values 1 6 1 -6 2 9 3 9 4 12 (2,9) (3,9) (4,12) (1,6)
Transcript text: Question 8 Which $x y$-pair in the relation shown in the table below causes the relation to not be a function? (In other words, which $x y$-pair could be removed to make the relation into a function) \begin{tabular}{|l|l|} \hline$x$-values & $y$-values \\ \hline 1 & 6 \\ \hline 1 & -6 \\ \hline 2 & 9 \\ \hline 3 & 9 \\ \hline 4 & 12 \\ \hline \end{tabular} $(2,9)$ $(3,9)$ $(4,12)$ $(1,6)$
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Solution

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Solution Steps

To determine which \( x y \)-pair causes the relation to not be a function, we need to identify if there is any \( x \)-value that is associated with more than one \( y \)-value. A function can only have one output for each input. In the given table, we should look for repeated \( x \)-values with different \( y \)-values.

Step 1: Identify Repeated \( x \)-Values

To determine which \( x y \)-pair causes the relation to not be a function, we first identify any repeated \( x \)-values in the given relation. A function must have unique \( y \)-values for each \( x \)-value. The relation is given as:

\[ \begin{align_} (1, 6), \\ (1, -6), \\ (2, 9), \\ (3, 9), \\ (4, 12) \end{align_} \]

Step 2: Check for Different \( y \)-Values

We observe that the \( x \)-value \( 1 \) is associated with two different \( y \)-values: \( 6 \) and \(-6\). This indicates that the relation is not a function because a function cannot have multiple outputs for a single input.

Step 3: Determine the Problematic Pair

The pair \((1, -6)\) is the one that can be removed to make the relation a function. By removing this pair, each \( x \)-value will have a unique \( y \)-value, satisfying the definition of a function.

Final Answer

\(\boxed{(1, -6)}\)

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