Answer the question and then write a short explanation. The...

Answer the question and then write a short explanation. The table shows the number of hazardous waste sites on the National Priority List for the Superfund program in 2008 for seven states in the top ten. If this correspondence is considered to be a function that pairs each state with its number of hazardous waste sites, is it one-to-one? If not, explain why. $$\begin{array}{|c|c|}\hline \text { State } & \text { Number of Sites } \\\hline \text { New Jersey } & 116 \\\hline \text { California } & 97 \\\hline \text { Pennsylvania } & 96 \\\hline \text { New York } & 86 \\\hline \text { Florida } & 52 \\\hline \text { Illinois } & 49 \\\hline \text { Texas } & 49 \\\hline\end{array}$$

Answer the question and then write a short explanation.
The table shows the number of hazardous waste sites on the National Priority List for the Superfund program in 2008 for seven states in the top ten. If this correspondence is considered to be a function that pairs each state with its number of hazardous waste sites, is it one-to-one? If not, explain why.
$$\begin{array}{|c|c|}\hline \text { State } & \text { Number of Sites } \\\hline \text { New Jersey } & 116 \\\hline \text { California } & 97 \\\hline \text { Pennsylvania } & 96 \\\hline \text { New York } & 86 \\\hline \text { Florida } & 52 \\\hline \text { Illinois } & 49 \\\hline \text { Texas } & 49 \\\hline\end{array}$$

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Key Concepts

Domain and Range

The domain of a function is the set of inputs (in this case, the states), and the range is the set of outputs (the number of hazardous waste sites). For a function to be one-to-one, each element of the range should correspond to exactly one element in the domain. Here, the occurrence of a repeated number in the range indicates that the relationship does not satisfy the one-to-one property.

Function Mapping

A function mapping is a rule that assigns each element in a set (known as the domain) exactly one element in another set (known as the codomain or range). In this context, the mapping pairs each state with a corresponding number of hazardous waste sites, meaning that every state has one and only one associated value.

Injective (One-to-One) Function

An injective or one-to-one function is a specific type of function where distinct elements in the domain map to distinct elements in the codomain. That is, if the function assigns the same output to two different inputs, then the function is not one-to-one. In the provided data, since two states have the same number of hazardous waste sites, the function is not injective.

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