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Answer:
To determine the relation that has the given domain {-5, -3, 0} and range {1, 2, 3, 4, 5, 6, 7, 8}, we need to consider the possible types of relations and their corresponding characteristics.
The key characteristics to consider are:
- Domain: the set of input values
- Range: the set of output values
Given the information provided, the relation that matches the described domain and range is:
A function
A function is a relation where each element in the domain is paired with exactly one element in the range.
In this case, the domain {-5, -3, 0} is mapped to a set of unique output values in the range {1, 2, 3, 4, 5, 6, 7, 8}.
For example, the function could be defined as:
f(x) = x + 6
Where:
- f(-5) = 1
- f(-3) = 3
- f(0) = 6
This satisfies the given domain and range requirements.
Other types of relations, such as a one-to-many relation or a many-to-many relation, would not have a domain and range that exactly match the provided information.
Therefore, the relation that has the given domain {-5, -3, 0} and range {1, 2, 3, 4, 5, 6, 7, 8} is a function.