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A function can be represented using a set of ordered pairs. Each ordered pair consists of two elements: the first element, or the input, and the second element, or the output. In the given function \(f=\{(-1,3),(4,7),(0,6),(2,2)\} \), the ordered pairs are:

• (-1, 3)
• (4, 7)
• (0, 6)
• (2, 2)

Note that the first number in each pair is the input, and the second number is the output. For instance, in the pair (2, 2), 2 is the input and 2 is the output. Ordered pairs help us see how each input is related to an output in the function.

In a function, each input is related to exactly one output. This relationship is evident through input-output pairs. Let's break down the function \(f\) mentioned earlier.
Given the set \(f=\{(-1,3),(4,7),(0,6),(2,2)\}\), each input (or x-value) is paired with an output (or y-value). For example:

• Input: -1, Output: 3
• Input: 4, Output: 7
• Input: 0, Output: 6
• Input: 2, Output: 2

To find \(f(2)\), we look for the pair with 2 as the input, which is (2, 2). Hence, \(f(2) = 2\). Similarly, to find \(f(-1)\), we look for the pair with -1 as the input, which is (-1, 3). Thus, \(f(-1) = 3\).

A function is essentially a mapping from one set (inputs) to another set (outputs). Each input is mapped to a specific output, and this can be visualized using ordered pairs. Let's revisit the given function \(f=\{(-1,3),(4,7),(0,6),(2,2)\}\). The mapping is as follows:

• -1 is mapped to 3
• 4 is mapped to 7
• 0 is mapped to 6
• 2 is mapped to 2

The function rule ensures that every input has only one output. This is what makes a function different from other types of relations. The function \(f\) gives a clear mapping of each input to its respective output, helping us see the relationship between the two sets. This mapping helps us easily find the function's value for specific inputs. For example, identifying how -1 maps to 3 helped us determine that \(f(-1) = 3\).