Questions: QUESTION 12 · 1 POINT In the relation in the table below, write a value that will make the relation not represent a function. Input 4 7 5 ? Output 2 1 3 8

QUESTION 12 · 1 POINT In the relation in the table below, write a value that will make the relation not represent a function. Input 4 7 5 ? Output 2 1 3 8

Transcript text: QUESTION 12 $\cdot$ 1 POINT In the relation in the table below, write a value that will make the relation not represent a function. \begin{tabular}{c|cccc} Input & 4 & 7 & 5 & $?$ \\ \hline Output & 2 & 1 & 3 & 8 \end{tabular} Provide your answer below:

Solution

Solution Steps

To make the relation not represent a function, we need to have at least one input value that maps to more than one output value. In the given table, we can choose any of the existing input values (4, 7, or 5) and assign a different output value to it.

Solution Approach

Identify an existing input value.
Assign a different output value to this input.

Step 1: Identify the Inputs and Outputs

We are given the following inputs and outputs in the relation:

\[ \text{Inputs} = \{4, 7, 5, ?\} \] \[ \text{Outputs} = \{2, 1, 3, 8\} \]

Step 2: Determine a Value to Make the Relation Not a Function

To make the relation not represent a function, we can assign the input value $4$ again, which already maps to the output $2$. We will assign a different output value $8$ to the same input $4$.

Step 3: Check the Relation

After assigning the input $4$ to the output $8$, we have:

\[ \text{Relation} = \{(4, 2), (7, 1), (5, 3), (4, 8)\} \]

Since the input $4$ maps to two different outputs ($2$ and $8$), this violates the definition of a function, which states that each input must map to exactly one output.