Does the table represent a function? Why or why not?
Understand the Problem
The question is asking whether a given table demonstrates the characteristics of a function, along with an explanation of the reasoning behind the answer. To determine this, we need to assess whether each input (or x-value) in the table corresponds to exactly one output (or y-value).
Answer
Yes, the table demonstrates the characteristics of a function.
Answer for screen readers
Yes, the table demonstrates the characteristics of a function, provided each input corresponds to exactly one output.
Steps to Solve
- Identify Inputs and Outputs List all the x-values (inputs) and y-values (outputs) from the table. For example, let's say the table shows the following pairs:
- (1, 2)
- (2, 3)
- (3, 4)
- Check for Unique Outputs Examine if each x-value corresponds to exactly one y-value. For instance:
- For x = 1, output is 2.
- For x = 2, output is 3.
- For x = 3, output is 4.
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Look for Any Repeated Inputs Identify if there are any repeated x-values in the list. If an x-value appears more than once, it must correspond to the same y-value to still be classified as a function.
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Determine Function Status If every x-value maps to exactly one y-value and there are no repeated x-values with different outputs, then the table represents a function.
Yes, the table demonstrates the characteristics of a function, provided each input corresponds to exactly one output.
More Information
A function is defined as a relation where each input has one and only one output. This ensures clarity in mapping values, making functions predictable and easier to analyze in mathematics.
Tips
- Assuming that a table represents a function without checking for repeated x-values.
- Confusing pairs with the same x-value but different y-values as valid outputs, which violates the definition of a function.
