Given A = {(1, 3)(-1, 5}(6, 4)}, B = {(2, 0)(4, 6)(-4, 5)(0, 0)} and C = {(1, 1)(0, 2)(0, 3)(0, 4)(-3, 5)}, answer the following multiple choice question:
From the list of sets A, B, and C above, choose the set of relations that correctly represents a function.
Sets A and C only
Set A only
Sets A and B only
Set A only
To determine which set of relations correctly represents a function, we need to check if each input value is associated with a unique output value.
Let's examine the sets A, B, and C:
Set A: {(1, 3)(-1, 5)(6, 4)}
- For input value 1, it is associated with output value 3.
- For input value -1, it is associated with output value 5.
- For input value 6, it is associated with output value 4.
All input values in set A have unique output values.
Set B: {(2, 0)(4, 6)(-4, 5)(0, 0)}
- For input value 2, it is associated with output value 0.
- For input value 4, it is associated with output value 6.
- For input value -4, it is associated with output value 5.
- For input value 0, it is associated with output value 0.
The input value 0 is associated with two different output values (0 and 6). Therefore, set B does not represent a function.
Set C: {(1, 1)(0, 2)(0, 3)(0, 4)(-3, 5)}
- For input value 1, it is associated with output value 1.
- For input value 0, it is associated with output values 2, 3, and 4.
- For input value -3, it is associated with output value 5.
The input value 0 is associated with multiple output values (2, 3, and 4). Therefore, set C does not represent a function.
Based on the analysis above, the set of relations that correctly represents a function is Set A only. So, the answer is "Set A only."
To determine which set represents a function, we need to check if there are any repeated first elements in any of the pairs within the set. In a function, each input (first element) can only be associated with one output (second element).
Let's go through each set:
Set A: {(1, 3), (-1, 5), (6, 4)}
- In set A, none of the first elements are repeated. Each input is associated with a unique output. Therefore, set A represents a function.
Set B: {(2, 0), (4, 6), (-4, 5), (0, 0)}
- In set B, the first element (0) is repeated twice, once with the output 0 and once with the output 4. Therefore, set B does not represent a function.
Set C: {(1, 1), (0, 2), (0, 3), (0, 4), (-3, 5)}
- In set C, the first element (0) is repeated three times, each associated with a different output. Therefore, set C does not represent a function.
Based on our analysis, the set of relations that correctly represents a function is:
Set A only
Therefore, the correct answer is:
Set A only.