A function is defined as {(0,1)(2,3)(5,8)(7,2)}. Issac is tasked to create one more ordered pair for the function. Which ordered pair can he add the set to keep it a function.
A. (7,0)
B. (1,3)
C. (0,2)
D. (5,3)
Please help! I'm really confused. :(
all you have to do is make sure that there are not two points with the same x-value.
B is the only choice whose x-value is not already used.
Answer is B.(1,3)
To determine which ordered pair Isaac can add to the set to keep it a function, we need to make sure that for each input (x-coordinate) in the set, there is only one corresponding output (y-coordinate).
Let's analyze the given set of ordered pairs:
{(0, 1), (2, 3), (5, 8), (7, 2)}
For an ordered pair (x, y) to be added to the set, the x-coordinate should not already exist in the set. This is because each x-coordinate must be unique in a function.
Let's check the answer choices one by one:
A. (7, 0): The x-coordinate 7 already exists in the set, so this is not a valid option.
B. (1, 3): The x-coordinate 1 does not exist in the set. So, this is a potential answer. But before selecting it, we need to make sure that no other answer fits better.
C. (0, 2): The x-coordinate 0 already exists in the set, so this is not a valid option.
D. (5, 3): The x-coordinate 5 already exists in the set, so this is not a valid option.
As we see, the only answer that works is B. So, Isaac can add the ordered pair (1, 3) to the set to keep it a function.
Therefore, the correct answer is B. (1, 3).
To determine which ordered pair Issac can add to the given set while keeping it a function, we need to understand what makes a set of ordered pairs a function.
In a function, no two different inputs (x-values) should have the same output (y-value). This means that each x-value can correspond to only one y-value.
Let's analyze the given set of ordered pairs: {(0,1), (2,3), (5,8), (7,2)}.
- (0,1): Here, the input 0 corresponds to the output 1.
- (2,3): The input 2 corresponds to the output 3.
- (5,8): The input 5 corresponds to the output 8.
- (7,2): The input 7 corresponds to the output 2.
Now, let's examine the answer choices and match them against the existing outputs:
A. (7,0): The input 7 is already assigned to the output 2. Therefore, we cannot add this pair as it would violate the function's definition.
B. (1,3): This pair introduces a new input 1 with the output 3, which is not already in the set. So, it is a valid pair that can be added to the set, keeping it a function.
C. (0,2): The input 0 is already assigned to the output 1. Therefore, we cannot add this pair as it would violate the function's definition.
D. (5,3): The input 5 is already assigned to the output 8. Therefore, we cannot add this pair as it would violate the function's definition.
Based on the analysis above, the correct answer is B. (1,3). Issac can add this ordered pair to the set, and it would still remain a function.