91Ó°ÊÓ

In mathematics, the domain of a relation is crucial because it represents all the possible input values for a given function or relation. Essentially, it's the set of all the 'x' values from the ordered pairs.

In the given problem, the ordered pairs are \[ \{(1,2),(2,4),(3,8),(4,16)\} \]. To determine the domain, we need to look at the first element of each ordered pair. Here they are:

• (1,2): first element is 1
• (2,4): first element is 2
• (3,8): first element is 3
• (4,16): first element is 4

Therefore, the domain of this relation is \[ \{1, 2, 3, 4\} \]. This means that the relation is defined and has values at these specific 'x' points. All other points are not considered within this relation, making it both unique and specific.

The range of a relation describes all the possible output values, which correspond to the 'y' values in the ordered pairs. To find the range, you need to extract and list the second element of each ordered pair.

In our exercise, the ordered pairs provided are \[ \{(1,2),(2,4),(3,8),(4,16)\} \]. So, we need to look at the second elements:

• (1,2): second element is 2
• (2,4): second element is 4
• (3,8): second element is 8
• (4,16): second element is 16

This gives us the range \[ \{2, 4, 8, 16\} \]. These are the results or outcomes that the relation produces. Any other output values are not part of this relation. By understanding both the domain and range, you can fully comprehend the scope of the relation.

Ordered pairs are a foundational concept in mathematics. They are written in the form (x, y), where 'x' is the first element and represents the input or domain, and 'y' is the second element and represents the output or range.

In our example, the set of ordered pairs is \[ \{(1,2),(2,4),(3,8),(4,16)\} \]. Here, each pair uniquely links a domain value with a range value, establishing a clear relationship.

Some important aspects to consider with ordered pairs include:

• The first part (x-value) always comes first and represents the domain.
• The second part (y-value) follows and represents the range.
• Ordered pairs are useful in graphing, mapping functions, and understanding relations.

Being careful with the order and understanding the distinction between 'x' and 'y' helps in accurately identifying the domain and range. Recognizing and correctly interpreting ordered pairs simplifies much of the work in mathematics involving functions and relations.