Problem 5 - Introductory Algebra for College Students

Question

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(-3,-3),(-2,-2),(-1,-1),(0,0)\\}$$

Step-by-Step Solution

Answer

Yes, the relation is a function. The domain is \{-3, -2, -1, 0\} and the range is also \{-3, -2, -1, 0\}.

Step 1: Identifying the function

The given relation is \{(-3,-3),(-2,-2),(-1,-1),(0,0)\}. We check each x-value (the first number in each pair) to ensure there is only one corresponding y-value (the second number in the pair) for it to be a function. Here, we see (-3,-3), (-2,-2), (-1,-1), and (0,0). For every x-value, there is only one unique y-value which means it is a function.

Step 2: Determine the domain

The domain is the set of all x-values or inputs. To find the domain, we list all the first numbers (x-values) from the ordered pairs. For this relation, the domain is \{-3, -2, -1, 0\}.

Step 3: Determine the range

The range is the set of all y-values or outputs. To find the range, we list all the second numbers (y-values) from the ordered pairs. For this relation, the range is \{-3, -2, -1, 0\}.