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Chapter 2: Problem 8

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

Short Answer

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

Step by step solution

01

Determine if the relation is a function

To determine if the relation is a function: Check if every first element (x-value) corresponds with only one second element (y-value). In this case, all x-values are unique, meaning that every x-value is paired with only one y-value. Therefore, the given relation is a function.
02

Determine the domain

The domain of a relation is the set of all first elements (x-values) in the ordered pairs. From the set \[\{(-7,-7),(-5,-5),(-3,-3),(0,0)\}\], the domain is \[-7, -5, -3, 0\].
03

Determine the range

The range of a function is the set of all second elements (y-values) in the ordered pairs. From the given set \[\{(-7,-7),(-5,-5),(-3,-3),(0,0)\}\], the range is \[-7, -5, -3, 0\].

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