Fill in the blank(s) to correctly complete each sentence. The domain of the relation { (3,5), (4, 9), (10, 13) } is _____.

Verified step by step guidance

1. Identify the definition of the domain in a relation, which is the set of all first elements (x-values) in the ordered pairs.
2. List the first elements from each ordered pair in the given relation: (3,5), (4,9), (10,13).
3. Extract the x-values from each ordered pair: 3, 4, and 10.
4. Combine these x-values into a set, as the domain is expressed as a set of numbers.
5. The domain of the relation is \( \{ 3, 4, 10 \} \).

Key Concepts

Domain of a Relation

The domain of a relation is the set of all first elements (or inputs) from the ordered pairs in the relation. In the given relation { (3,5), (4, 9), (10, 13) }, the domain consists of the values 3, 4, and 10. Understanding the domain is crucial for analyzing the behavior of functions and relations.

Ordered Pairs

An ordered pair is a pair of elements where the order matters, typically written as (x, y). In the context of relations, the first element represents the input, while the second element represents the output. Recognizing ordered pairs helps in identifying the structure of a relation and its components.

Set Notation

Set notation is a mathematical way to describe a collection of distinct objects, often enclosed in curly braces. In this case, the relation is expressed using set notation, which allows for a clear representation of the pairs involved. Familiarity with set notation is essential for understanding how to manipulate and interpret relations in algebra.