Which ordered pair could be removed to make a function?
{(1,3) (2,4) (3,4) (3,6) (5,10) (6,3)}
A) (2,4)
B) (3,4)
C (1,3)
D) (6,3)
Nope. The 1st element cannot be repeated. (3,4) or (3,6) has to go. So, B.
I got D, can you please check this?
Well, let's see. A function can only have one output value for each input value. So, if there is more than one ordered pair with the same input value but different output values, we have a problem.
Looking at the options, if we remove (3,4), we still have (3,6) with the same input value of 3. So, that doesn't work.
If we remove (2,4), we no longer have a pair with an input value of 2. Oops!
If we remove (6,3), we still have (6,3) as the only pair with an input value of 6, so that's not it.
Lastly, if we remove (1,3), we still have (2,4) with the same input value of 2. Darn!
So, it seems we can't remove any ordered pair from this set to make it a function. We're stuck with all of them! Better luck next time!
To determine which ordered pair could be removed to make a function, we need to first understand the definition of a function. A function is a relation where each input value (x-value) is associated with exactly one output value (y-value). In other words, no two different x-values can be associated with the same y-value.
Let's examine the given set of ordered pairs: {(1,3), (2,4), (3,4), (3,6), (5,10), (6,3)}.
We can see that the ordered pair (3,4) violates the definition of a function because the x-value of 3 is associated with two different y-values, 4 and 6. Therefore, if we remove the ordered pair (3,4), the set will satisfy the definition of a function.
So, the correct answer is B) (3,4).
To determine which ordered pair could be removed to make a function, we need to understand what defines a function.
In mathematics, a function is a relation in which each input has exactly one output. This means that for every unique x-value in the set of ordered pairs, there should be only one y-value associated with it.
To find the ordered pair that can be removed to make the set of ordered pairs a function, we need to check if there are any repeated x-values with different y-values.
Let's analyze the given set of ordered pairs:
{(1,3), (2,4), (3,4), (3,6), (5,10), (6,3)}
By examining the set, we can see that the x-value of 3 appears twice: (3,4) and (3,6). Since there are two different y-values associated with the x-value of 3, we cannot remove either (3,4) or (3,6) to make it a function.
Therefore, the answer to the question is none of the options given (A) (2,4), (B) (3,4), (C) (1,3), or (D) (6,3) can be removed to make the set of ordered pairs a function.