Question

determine whether the following relation is a function. give the domain and range for the relation.\\{(-7,-7), (5,5), (-9,-9), (1,1)\\}\
does the given relation represent a function?\
\bigcirc yes\
\bigcirc no

Explanation:

Step1: Recall function definition

A relation is a function if each input (x - value) has exactly one output (y - value). In a set of ordered pairs \((x,y)\), we check if any \(x\) - value is repeated.
The given relation is \(\{(-7,-7),(5,5),(-9,-9),(1,1)\}\). The \(x\) - values (inputs) are \(-7\), \(5\), \(-9\), and \(1\). Each \(x\) - value appears only once. So, for each input, there is exactly one output.

Step2: Determine domain and range (optional for the function check, but part of the problem)

• Domain: The set of all \(x\) - values in the ordered pairs. So, domain is \(\{-7,5,-9,1\}\).
• Range: The set of all \(y\) - values in the ordered pairs. So, range is \(\{-7,5,-9,1\}\) (since each \(y\) - value is equal to its corresponding \(x\) - value here). But for the function check, we only needed to see that no \(x\) - value is repeated.

Answer:

Yes (because each \(x\) - value in the ordered pairs \((-7, - 7),(5,5),(-9,-9),(1,1)\) is unique, meaning each input has exactly one output, so the relation is a function).
The domain of the relation is \(\{-7,5,-9,1\}\) and the range of the relation is \(\{-7,5,-9,1\}\).