Which of the following would NOT represent a function?
a) {(1, 3), (2, 5), (5, 3), (7, 10)}
b) ((-1, 4), (2, 4), (0, 4), (9,4)]
c) ((-3,-2). (-1, 0), (3, 7), (6, 1)}
d) {(1, 12), (2, 8), (3, 1), (1,-4)]
a) {(1, 3), (2, 5), (5, 3), (7, 10)}
This does represent a function because each input value (x-value) is associated with exactly one output value (y-value).
b) ((-1, 4), (2, 4), (0, 4), (9,4)]
This also represents a function because each input value (x-value) is associated with exactly one output value (y-value).
c) ((-3,-2). (-1, 0), (3, 7), (6, 1)}
This represents a function because each input value (x-value) is associated with exactly one output value (y-value).
d) {(1, 12), (2, 8), (3, 1), (1,-4)]
This does NOT represent a function because the input value 1 is associated with two different output values (12 and -4).
A function is a relation between a set of inputs and a set of outputs, where each input has only one corresponding output. In other words, for every input value, there should be only one possible output value.
To determine which of the given options represents a function, we need to check if each input value is paired with a unique output value. Let's analyze each option:
a) {(1, 3), (2, 5), (5, 3), (7, 10)}
This option represents a function because each input value (1, 2, 5, 7) is paired with a unique output value (3, 5, 3, 10).
b) ((-1, 4), (2, 4), (0, 4), (9, 4)]
This option also represents a function because each input value (-1, 2, 0, 9) is paired with a unique output value (4).
c) ((-3, -2), (-1, 0), (3, 7), (6, 1)]
This option represents a function as well since each input value (-3, -1, 3, 6) is paired with a unique output value (-2, 0, 7, 1).
d) {(1, 12), (2, 8), (3, 1), (1, -4)]
This option does NOT represent a function because the input value 1 is paired with two different output values (12 and -4). Each input value must have only one corresponding output value for it to be a function.
Therefore, the answer is option d) {(1, 12), (2, 8), (3, 1), (1, -4)}.
To determine which of the given options does not represent a function, we need to check if each option satisfies the definition of a function.
A function is a relation in which each input has exactly one output.
Let's analyze each option:
a) {(1, 3), (2, 5), (5, 3), (7, 10)}:
Every input (x-value) in this option corresponds to exactly one output (y-value), which satisfies the definition of a function.
b) ((-1, 4), (2, 4), (0, 4), (9,4)]:
Once again, in this option, each input (x-value) corresponds to exactly one output (y-value), so it represents a function.
c) ((-3,-2). (-1, 0), (3, 7), (6, 1)):
Similar to the previous two options, each input (x-value) has exactly one output (y-value), so it represents a function.
d) {(1, 12), (2, 8), (3, 1), (1,-4)]:
Here, we have a problem. The input value 1 is associated with two different output values (12 and -4). According to the definition of a function, each input can only have one output. Therefore, option d) does NOT represent a function.
In conclusion, option d) {(1, 12), (2, 8), (3, 1), (1,-4)]} does not represent a function since the input value 1 is associated with two different output values.