Questions: Relation 4 Domain Range 1 9 -1 1 -8 1 5 1 2 9 Function Not a function

Transcript text: Relation 4 \begin{tabular}{|c|c|} \hline Domain & Range \\ \hline 1 & 9 \\ \hline-1 & 1 \\ \hline-8 & 1 \\ \hline 5 & 1 \\ \hline 2 & 9 \\ \hline \end{tabular} Function Not a function

Solution

Solution Steps

To determine if a relation is a function, we need to check if each element in the domain maps to exactly one element in the range. If any element in the domain maps to more than one element in the range, it is not a function.

Step 1: Define the Relation

The given relation is represented as a set of ordered pairs: \[ \text{relation} = \{(1, 9), (-1, 1), (-8, 1), (5, 1), (2, 9)\} \]

Step 2: Check for Functionality

To determine if this relation is a function, we need to verify that each element in the domain maps to exactly one element in the range. We will create a mapping from the domain to the range.

Step 3: Create the Mapping

The mapping derived from the relation is: \[ \text{mapping} = \{1: 9, -1: 1, -8: 1, 5: 1, 2: 9\} \] Here, each domain element corresponds to a single range element.

Step 4: Analyze the Mapping

Since each domain element maps to only one range element, we conclude that the relation satisfies the definition of a function.