Indicate whether the relation a function or not a function. Justify your answer.

To determine whether a relation is a function, we need to consider the definition of a function. A relation is a function if every input (or element from the domain) is associated with exactly one output (or element from the range). This means that for each unique value of the input, there must not be multiple corresponding values for the output.

Here are the steps to analyze a relation and justify whether it is a function:

1. Identify the Inputs and Outputs: Look at the sets of inputs (domain) and outputs (range) associated with the relation.

2. Check for Uniqueness: For each input, check if there is more than one output. If an input corresponds to two or more different outputs, the relation is not a function.

3. Examples:

   • If the relation is represented as a set of ordered pairs, such as \((1, 2)\), \((1, 3)\), and \((2, 4)\):
     • Input \(1\) has outputs \(2\) and \(3\) → Not a function.
     • Inputs \(2\) has output \(4\) → This input-output pair is fine, but since the first input fails, the entire relation is not a function.
   • If the relation is represented as a set of points on a graph, check for vertical lines (the vertical line test). If any vertical line intersects the graph at more than one point, the relation is not a function.

4. Conclusion: Based on the above checks, you can declare the relation as a function or not.

If you provide a specific relation (like a set of points, equations, or a description), I could analyze it for you and justify whether it's a function or not!