91Ó°ÊÓ

In algebra, the domain of a relation refers to the complete set of possible input values. These are usually the x-values in a set of ordered pairs. It is helpful to think of the domain as all the values you can plug into a function or relation.
For instance, consider the relation given by the set of ordered pairs \((3,-6), (1,4), (-2,-2)\). To find the domain, you just need to look at the x-values from each pair.
Here, the x-values are 3, 1, and -2. To express the domain, list these values without repetition. Therefore, the domain is \{3, 1, -2\}.

• Always check if the relation defines any constraints on x-values. If so, they may affect the domain.
• Remember that the domain can consist of any kind of number, including integers, fractions, or even irrational numbers.

The range in algebra represents the set of possible output values, typically the y-values, in a relation. It helps to understand what values a relation can produce or map to.
Taking the same set of ordered pairs \((3,-6), (1,4), (-2,-2)\) as an example, you need to identify the y-values.
These values are -6, 4, and -2. Just like with the domain, list the unique values without repetition to find the range. Hence, the range is \{-6, 4, -2\}.

• Note that the range is dependent on the relation itself, meaning different relations can have entirely different ranges.
• In some contexts, it may be helpful to express the range in terms of inequalities or specific intervals, particularly with continuous functions.

Ordered pairs are a foundational concept in algebra, consisting of two elements written in a specific order. Typically, they are denoted as \((x, y)\), where x is the first element and y is the second. The order is crucial because it conveys the meaning, with (3, -6) being distinct from (-6, 3).
In the context of a relation, ordered pairs help us understand the input-output relationship. For each x-value in the domain, there is a corresponding y-value in the range.
Consider how ordered pairs \((3, -6), (1, 4), (-2, -2)\) work in our exercise:

• They map the input x-value to a specific output y-value, defining a relation between these values.
• Ordered pairs are a simple yet powerful way to represent mathematical relations and functions.

When working with ordered pairs, always ensure you clearly distinguish between the elements, maintaining their position and order to preserve their meaning.