Choose if each statement is True or False.
{(1, 2), (3, 6), (4, -7), (6, -10)} is a function: true or false
{(1,1), (2, 2), (3, 3), (4,4)} is a function: true or false
{(1, 3), (2, 5), (7, 9), (2, 12)} is a function: true or false
{(1, 8), (2, 8), (3, 8), (4,8)} is a function: true or false
function iff no input value is used more than once.
In order to determine whether the given sets are functions or not, we need to understand the definition of a function.
A function is a mapping from a set of inputs (the domain) to a set of outputs (the range), such that each input is associated with exactly one output. In other words, for each element in the domain, there must be a unique corresponding element in the range.
Let's analyze each statement:
1. {(1, 2), (3, 6), (4, -7), (6, -10)} is a function: False
To determine if this set is a function, we need to check if each input (the first element of each ordered pair) is associated with a unique output (the second element of each ordered pair). In this case, the input "2" is associated with both the output "3" and the output "-7", which violates the definition of a function. Thus, this statement is False.
2. {(1,1), (2, 2), (3, 3), (4,4)} is a function: True
In this set, each input (the first element of each ordered pair) is associated with a unique output (the second element of each ordered pair). For example, the input "2" is associated with the output "2". Since there are no repetitions in the inputs, this set is a function. Thus, this statement is True.
3. {(1, 3), (2, 5), (7, 9), (2, 12)} is a function: False
In this set, the input "2" is associated with both the output "5" and the output "12", violating the definition of a function. Therefore, this set is not a function. Thus, this statement is False.
4. {(1, 8), (2, 8), (3, 8), (4,8)} is a function: True
In this set, each input (the first element of each ordered pair) is associated with a unique output (the second element of each ordered pair). For example, the input "2" is associated with the output "8". Since there are no repetitions in the inputs, this set is a function. Thus, this statement is True.