Question

1. the set of ordered pairs below is a function. {(5,0) (1, 3) (7,6) (2,4) (x, 9) } select all the following that could be the value of the x in the fifth ordered pair so that it is a function. 0 1 2 3 4 5 6 7

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value). So, for the given set of ordered pairs \(\{(5,0),(1,3),(7,6),(2,4),(x,9)\}\) to be a function, the \(x\) - value in the fifth ordered pair must not be equal to the \(x\) - values of the existing ordered pairs.
The existing \(x\) - values are \(5\), \(1\), \(7\), and \(2\).

Step2: Check each option

• Option \(0\): \(0\) is not in the set \(\{5,1,7,2\}\), so \(x = 0\) is valid.
• Option \(1\): \(1\) is already an \(x\) - value (from the pair \((1,3)\)), so \(x = 1\) is not valid.
• Option \(2\): \(2\) is already an \(x\) - value (from the pair \((2,4)\)), so \(x = 2\) is not valid.
• Option \(3\): \(3\) is not in the set \(\{5,1,7,2\}\), so \(x = 3\) is valid.
• Option \(4\): \(4\) is not in the set \(\{5,1,7,2\}\), so \(x = 4\) is valid.
• Option \(5\): \(5\) is already an \(x\) - value (from the pair \((5,0)\)), so \(x = 5\) is not valid.
• Option \(6\): \(6\) is not in the set \(\{5,1,7,2\}\), so \(x = 6\) is valid.
• Option \(7\): \(7\) is already an \(x\) - value (from the pair \((7,6)\)), so \(x = 7\) is not valid.

Answer:

A. \(0\), B. \(3\), C. \(4\), D. \(6\) (assuming the options are labeled as 0: A, 1: B, 2: C, 3: D, 4: E, 5: F, 6: G, 7: H. But following the instruction to include identifiers and text, the valid ones are: 0, 3, 4, 6. So the answer is the options with values 0, 3, 4, 6. If we consider the options as presented (0,1,2,3,4,5,6,7) with their respective numbers, the valid \(x\) values are 0, 3, 4, 6.