Question

(4) he was standing still.
2 given the relation: {(0,4), (2,6), (4,8), (x,7)}
which value of x will make this relation a function?
(1) 0
(2) 2
(3) 6
(4) 4

Explanation:

Step1: Recall Function Definition

A function is a relation where each input (x - value) has exactly one output (y - value). So, we need to ensure that the x - value we choose for the ordered pair \((x,7)\) is not already used as an x - value in the other ordered pairs \((0,4)\), \((2,6)\), and \((4,8)\).

Step2: Check Existing x - Values

The existing x - values in the relation are \(0\), \(2\), and \(4\). So, \(x\) cannot be \(0\), \(2\), or \(4\) because that would mean an x - value is mapped to more than one y - value (violating the function definition).

Step3: Evaluate the Options

• Option 1: \(x = 0\) is already used (from \((0,4)\)), so it's invalid.
• Option 2: \(x = 2\) is already used (from \((2,6)\)), so it's invalid.
• Option 3: \(x = 6\) is not one of the existing x - values (\(0\), \(2\), \(4\)), so it is valid.
• Option 4: \(x = 4\) is already used (from \((4,8)\)), so it's invalid.

Answer:

1. 6