To determine whether a given relation is a function, we need to check if each input value (domain) maps to exactly one unique output value (range). That means no input value should have more than one corresponding output value.
Given the relation:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Input} & \text{Output} \\
\hline -3 & 6 \\
\hline -2 & 4 \\
\hline -1 & 2 \\
\hline 0 & 0 \\
\hline 1 & 2 \\
\hline
\end{array}
\][/tex]
We can check the input values to ensure each one maps to a single output:
1. Input: -3 maps to Output: 6.
2. Input: -2 maps to Output: 4.
3. Input: -1 maps to Output: 2.
4. Input: 0 maps to Output: 0.
5. Input: 1 maps to Output: 2.
These are the only pairs in the relation.
To summarize:
- Input -3 appears once and maps to 6.
- Input -2 appears once and maps to 4.
- Input -1 appears once and maps to 2.
- Input 0 appears once and maps to 0.
- Input 1 appears once and maps to 2.
Since each input maps to exactly one output and there are no repeated input values mapping to different outputs, the given relation satisfies the definition of a function.
Hence, the given relation is a function.
