Question

1. each set of ordered pairs represents a function. which set of ordered pairs would still represent a function if the values of the x-coordinates and the values of the y-coordinates were reversed?

a {(1, 4), (2, 3), (3, 1), (4, 3)}
b {(1, 2), (2, 2), (3, 3), (4, 3)}
c {(1, 1), (2, 1), (3, 1), (4, 1)}
d {(1, 2), (2, 3), (3, 4), (4, 5)}

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value). When we reverse the coordinates of an ordered pair \((x,y)\) to \((y,x)\), we need to check if the new relation (with reversed coordinates) is also a function, i.e., each new \(x\) - value (original \(y\) - value) has exactly one new \(y\) - value (original \(x\) - value).

Step2: Analyze Option A

Original set: \(\{(1,4),(2,3),(3,1),(4,3)\}\)
Reversed set: \(\{(4,1),(3,2),(1,3),(3,4)\}\)
In the reversed set, the \(x\) - value \(3\) is paired with \(2\) and \(4\). So, it is not a function.

Step3: Analyze Option B

Original set: \(\{(1,2),(2,2),(3,3),(4,3)\}\)
Reversed set: \(\{(2,1),(2,2),(3,3),(3,4)\}\)
In the reversed set, the \(x\) - value \(2\) is paired with \(1\) and \(2\), and the \(x\) - value \(3\) is paired with \(3\) and \(4\). So, it is not a function.

Step4: Analyze Option C

Original set: \(\{(1,1),(2,1),(3,1),(4,1)\}\)
Reversed set: \(\{(1,1),(1,2),(1,3),(1,4)\}\)
In the reversed set, the \(x\) - value \(1\) is paired with \(1\), \(2\), \(3\), and \(4\). So, it is not a function.

Step5: Analyze Option D

Original set: \(\{(1,2),(2,3),(3,4),(4,5)\}\)
Reversed set: \(\{(2,1),(3,2),(4,3),(5,4)\}\)
In the reversed set, each \(x\) - value (\(2\), \(3\), \(4\), \(5\)) has exactly one \(y\) - value (\(1\), \(2\), \(3\), \(4\)) respectively. So, it is a function.

Answer:

D. \(\{(1, 2), (2, 3), (3, 4), (4, 5)\}\)