Determine if the correspondence is a function. Domain $$ \quad $$ a set of numbers Correspondence $$ \begin{array}{ll} ext { the square of each number } \ ext { Range set of numbers }\end{array} $$ Is this correspondence a function? Yes No

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Determine if the correspondence is a function. Domain $$ \quad $$ a set of numbers Correspondence $$ \begin{array}{ll}	ext { the square of each number } \ 	ext { Range set of numbers }\end{array} $$ Is this correspondence a function? Yes No

UpStudy AI · Accepted Answer

Yes, the correspondence described is a function. Here's why:

### Definition of a Function
A **function** is a relation between a set of inputs (domain) and a set of possible outputs (range) where **each input is related to exactly one output**.

### Given Correspondence
- **Domain:** A set of numbers.
- **Correspondence:** The square of each number.
- **Range:** Set of numbers resulting from the squaring process.

### Analysis
- **Uniqueness:** For every number $$ x $$ in the domain, squaring it ($$ x^2 $$) produces exactly one output.
- **Well-Defined:** There is no ambiguity in the output; each input has a clear, single output.

### Conclusion
Since every input number is associated with one and only one output (its square), the correspondence satisfies the definition of a function.

**Answer:**  
Yes
Yes, the correspondence is a function because each number in the domain is paired with exactly one number in the range by squaring it.

Determine if the correspondence is a function. Domain \( \quad \) a set of numbers Correspondence \( \begin{array}{ll}\text { the square of each number } \\ \text { Range set of numbers }\end{array} \) Is this correspondence a function? Yes No

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