Is the relation a function? Explain.
Understand the Problem
The question is asking whether the given set of ordered pairs represents a function, which involves determining if each input (time in minutes) corresponds to exactly one output (temperature). We will analyze the pairs to check for uniqueness of inputs.
Answer
Yes, the relation is a function.
Answer for screen readers
Yes, the relation is a function.
Steps to Solve
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Identify Inputs and Outputs List all the inputs (the first element of each ordered pair) and the outputs (the second element):
Inputs: 0, 5, 10, 15, 20, 25
Outputs: 15, 20, 50, 80, 100 -
Check for Unique Inputs Examine the list of inputs to ensure that no input value repeats.
In this case:
- Every input is unique (0, 5, 10, 15, 20, 25).
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Define a Function
A relation is a function if each input corresponds to exactly one output. Since all inputs in our list correspond to one unique output, we conclude:
Yes, each time (input) corresponds to exactly one temperature (output).
Yes, the relation is a function.
More Information
In functions, each input value can only map to one output value, making them essential in mathematics for representing relationships. This ordered pair representation helps visualize how one variable affects another.
Tips
- Assuming a relation is a function without checking if inputs repeat.
- Miscounting or overlooking values when identifying unique inputs.
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