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An ordered pair is simply a set of two values that are grouped together in a specific order, usually represented as \(x, y\). The first value in this pair is the 'x-value,' and the second value is the 'y-value.' In the context of functions, these pairs help us to understand how different inputs map to outputs. Each ordered pair represents a connection: the first element is often the input from a domain, while the second is the output within the range.

In our example function \(h:\{(-5,2),(-4,2),(-3,2),(-2,2),(-1,2)\}\), each of these is an ordered pair. We can think of them like pairs of coordinates, where 'x' is -5, -4, -3, -2, -1, and they all map to the same 'y' value, which is 2.

The domain of a function is a fundamental concept in mathematics. It refers to all the possible input values (or x-values) that the function can accept without causing an error.

In easier terms, the domain is a list of the x-values found in the ordered pairs of a function. For a given set of ordered pairs, the domain is formed by collecting all the first elements from each pair. In our example \(h:\{(-5,2),(-4,2),(-3,2),(-2,2),(-1,2)\}\), the domain is:

• -5
• -4
• -3
• -2
• -1

These represent all the inputs of the function, and any calculation involving this function will work with these numbers.

Understanding the range of a function involves looking at the possible outputs (or y-values) a function can produce. When we talk about the range, we are referring to the set of second elements from the ordered pairs. It can be seen as all the resultant values that come out when you plug the domain values into the function's rule or equation.

In the example at hand, \(h:\{(-5,2),(-4,2),(-3,2),(-2,2),(-1,2)\}\), the range is simply {2}. Here, each ordered pair shares the same y-value, which means regardless of the x-value, the function consistently outputs 2. Thus, our range highlights this uniformity and consists of this solitary value.