Is this relation a function? Justify your answer.
Understand the Problem
The question is asking whether a given relation satisfies the criteria to be classified as a function. A relation is considered a function if each input (or 'x' value) has exactly one output (or 'y' value). To justify the answer, one would typically analyze the relation's pairs to check if any input corresponds to multiple outputs.
Answer
The relation is not a function.
Answer for screen readers
The relation is not a function because the input 1 corresponds to multiple outputs (2 and 4).
Steps to Solve
- List the ordered pairs of the relation
Identify the pairs that constitute the given relation. For example, let's suppose the relation is represented as: {(1, 2), (2, 3), (1, 4)}.
- Identify the unique inputs (x values)
Look at the first components (the x values) of each ordered pair to form a list of unique inputs. For our example, we would have the unique inputs as {1, 2}.
- Check the outputs for each input
For each unique input, check how many different outputs (y values) correspond to that input.
For input 1, we see it corresponds to outputs 2 and 4.
For input 2, we have it corresponding to output 3.
- Determine if each input has exactly one output
If any input has more than one corresponding output, the relation does not qualify as a function. In our example, since input 1 corresponds to both 2 and 4, we conclude that this relation is not a function.
The relation is not a function because the input 1 corresponds to multiple outputs (2 and 4).
More Information
A relation failing to meet the criteria of having one output for each input simply cannot be classified as a function. This is fundamental in mathematics, particularly in algebra where functions are often used to represent relationships between variables.
Tips
A common mistake is to overlook pairs with the same input but different outputs. Always check every input in the set of ordered pairs to ensure that this criterion is strictly followed.
