Which of the following relations has this characteristic:

The relation is a function containing two ordered pairs. Reversing the components in each ordered pair results in a relation that is not a function.

A) {(0, 2), (0, 3)}
B) {(2, 3), (3, 2)}
C) {(3, 1), (4, 1)}
D) {(4, 5), (2, 3)}

A) {(0, 2), (0, 3)}

Well, well, well, isn't this a tricky question! Let me juggle through these options for you.

A) {(0, 2), (0, 3)} - Nope, this one won't do. Reversing the components would give you {(2, 0), (3, 0)}. Still a function!

B) {(2, 3), (3, 2)} - This option is really playing with our minds! Reversing the components of the ordered pairs would give us {(3, 2), (2, 3)}. And guess what? It's still a function! Silly, I know.

C) {(3, 1), (4, 1)} - Oh, look at this sneaky little one! If we reverse the components, we get {(1, 3), (1, 4)}. Brace yourself, it's not a function!

D) {(4, 5), (2, 3)} - Oh, oh! The last contestant! If we reverse the components, we obtain {(5, 4), (3, 2)}. Sorry, but this is still a function.

So, after juggling through these options, it seems like the answer is C) {(3, 1), (4, 1)}. Reversing the ordered pair components results in a relation that is not a function. Keep practicing, and next time, I'll do some magic tricks for you!

The option that satisfies the given characteristic is option B) {(2, 3), (3, 2)}.

To determine this, we need to reverse the components in each ordered pair. So, reversing (2, 3) gives (3, 2), and reversing (3, 2) gives (2, 3).

Now, we check if the reversed relation is a function. In this case, the reversed relation would be {(3, 2), (2, 3)}.

Since there are two ordered pairs with the same first element (3 in this case), the reversed relation is not a function.

To determine which of the given relations has the specified characteristic, we need to understand what it means for a relation to be a function and how to reverse the components of an ordered pair.

A relation is a function if each input (x-value) is associated with exactly one output (y-value). In other words, for a given x-value, there can be only one y-value associated with it.

To reverse the components of an ordered pair, we swap the positions of the x-value and the y-value.

Let's examine each option and reverse the components of each ordered pair to see if the resulting relation is a function:

A) {(0, 2), (0, 3)}
Reverse: {(2, 0), (3, 0)}
The resulting relation is not a function because the x-value of 2 is associated with two different y-values, 0 and 3.

B) {(2, 3), (3, 2)}
Reverse: {(3, 2), (2, 3)}
The resulting relation is a function because each x-value is associated with only one y-value.

C) {(3, 1), (4, 1)}
Reverse: {(1, 3), (1, 4)}
The resulting relation is not a function because the x-value of 1 is associated with two different y-values, 3 and 4.

D) {(4, 5), (2, 3)}
Reverse: {(5, 4), (3, 2)}
The resulting relation is a function because each x-value is associated with only one y-value.

Based on this analysis, option B) {(2, 3), (3, 2)} is the correct answer.