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 any of the existing \(x\) - values in the other ordered pairs.

Step2: Identify existing x - values

The existing \(x\) - values in the ordered pairs are \(5\), \(1\), \(7\), and \(2\).

Step3: Determine valid x - values

We need to find the values from the list \(0,1,2,3,4,5,6,7\) that are not equal to \(5\), \(1\), \(7\), or \(2\).

• For \(x = 0\): \(0\) is not in \(\{5,1,7,2\}\), so it is valid.
• For \(x = 1\): \(1\) is in \(\{5,1,7,2\}\), so it is not valid.
• For \(x = 2\): \(2\) is in \(\{5,1,7,2\}\), so it is not valid.
• For \(x = 3\): \(3\) is not in \(\{5,1,7,2\}\), so it is valid.
• For \(x = 4\): \(4\) is not in \(\{5,1,7,2\}\), so it is valid.
• For \(x = 5\): \(5\) is in \(\{5,1,7,2\}\), so it is not valid.
• For \(x = 6\): \(6\) is not in \(\{5,1,7,2\}\), so it is valid.
• For \(x = 7\): \(7\) is in \(\{5,1,7,2\}\), so it is not valid.

Answer:

0, 3, 4, 6