Problem 8 - Precalculus Essentials

Question

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(-7,-7),(-5,-5),(-3,-3),(0,0)\\}$$

Step-by-Step Solution

Answer

The given relation is a function. The domain of the function is \{0, -3, -5, -7\} and the range is also \{0, -3, -5, -7\}.

Step 1: Identify If the Relation is a Function

A relation can be considered a function if each x-value or input corresponds to a unique y-value or output. No x-value should map to more than one y-value. Looking at the ordered pairs (-7,-7),(-5,-5),(-3,-3),(0,0), we can observe that every x-value corresponds to one y-value. Hence, the relation can be considered as a function.

Step 2: Determine the Domain of the Function

The domain of a function is made up of all the x-values from the ordered pairs. Here, the domain is \(-7, -5, -3, 0\). Therefore, the domain of this relation, when listed in ascending order, is \{0, -3, -5, -7\}.

Step 3: Determining the Range of the Function

The range of the function encompasses all of the y-values from the ordered pairs. Here, the y-values are \(-7, -5, -3, 0\). Hence, in ascending order, the range of the relation is \{0, -3, -5, -7\}.