The problem asks us to identify which of the given relations are functions. A relation is a function if each input has exactly one output. We are given four tables of input-output pairs and need to determine which represent functions.
2025/3/12
1. Problem Description
The problem asks us to identify which of the given relations are functions. A relation is a function if each input has exactly one output. We are given four tables of input-output pairs and need to determine which represent functions.
2. Solution Steps
A relation is a function if and only if each input value is associated with a unique output value. In other words, there cannot be two pairs with the same input but different outputs.
Table 1:
Input: 13, Output: 4
Input: 9, Output: 8
Input: 19, Output: -2
Input: 9, Output: 12
Input: -4, Output: 20
The input 9 is associated with two different outputs (8 and 12). Therefore, this is not a function.
Table 2:
Input: 14, Output: -18
Input: 20, Output: 17
Input: 6, Output: 18
Input: 10, Output: 18
Input: 12, Output: 18
All inputs are unique, so each input has only one output. This is a function.
Table 3:
Input: 10, Output: 7
Input: 4, Output: 17
Input: 2, Output: 6
Input: 9, Output: 18
Input: 17, Output: 12
All inputs are unique, so each input has only one output. This is a function.
Table 4:
Input: 3, Output: 5
Input: 7, Output: 5
Input: -5, Output: 8
Input: -3, Output: 10
Input: 7, Output: -8
The input 7 is associated with two different outputs (5 and -8). Therefore, this is not a function.
3. Final Answer
The relations that are functions are:
Table 2
Table 3