Determine whether the tables in Exercises 11 through 18...

Determine whether the tables in Exercises 11 through 18 represent functions or not. Assume that the input is in the left column or top row. Explain your answer. $$\begin{array}{|c|c|}\hline \text { Years in College } & \text { Credits Earned } \\\hline 1 & 30 \\2 & 75 \\1 & 36 \\3 & 60 \\4 & 120 \\5 & 100 \\1.5 & 50 \\\hline\end{array}$$

Determine whether the tables in Exercises 11 through 18 represent functions or not. Assume that the input is in the left column or top row. Explain your answer.
$$\begin{array}{|c|c|}\hline \text { Years in College } & \text { Credits Earned } \\\hline 1 & 30 \\2 & 75 \\1 & 36 \\3 & 60 \\4 & 120 \\5 & 100 \\1.5 & 50 \\\hline\end{array}$$

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Key Concepts

Uniqueness Criterion

This principle requires that for each input in the relation, there is only one corresponding output. A violation of the uniqueness criterion, such as when the same input is paired with different outputs, means the relation is not a function.

Domain

The domain is the set of all possible input values for which the relation is defined. Recognizing the domain is crucial because it helps in identifying if there are any repeated inputs with differing outputs.

Function Definition

A function is a relation that assigns exactly one output to each input. This concept is the foundation for determining if a relation described by a table is a function, as no input should have more than one corresponding output.

Input-Output Mapping

This concept refers to the association between every element in the input set (domain) and a unique element in the output set (range). In verifying if a table represents a function, one must ensure that each input consistently yields a single output.

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