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)}
d) {(1, 12), (2, 8), (3, 1), (1, -4)}
In this option, the x-value of (1, 12) is repeated twice, with different y-values. A function can only have one output for each input, so this option does not represent a function.
d) {(1, 12), (2, 8), (3, 1), (1, -4)}
To determine which of the given sets does not represent a function, we need to understand what a function is. A function is a relation in which each input (or x-value) is associated with only one output (or y-value).
Let's analyze each set of ordered pairs:
a) {(1, 3), (2, 5), (5, 3), (7, 10)}: This set is a function since each x-value corresponds to exactly one y-value.
b) {(-1, 4), (2, 4), (0, 4), (9, 4)}: This set is also a function. In this case, all the ordered pairs have the same y-value of 4, but since each x-value is associated with only one y-value, it still satisfies the definition of a function.
c) {(-3, -2), (-1, 0), (3, 7), (6, 1)}: This set is a function since each x-value has a unique y-value associated with it.
d) {(1, 12), (2, 8), (3, 1), (1, -4)}: This set is NOT a function because the x-value of 1 is associated with two different y-values, 12 and -4. This violates the definition of a function, as each input must have only one corresponding output.
Therefore, the set that does NOT represent a function is option d) {(1, 12), (2, 8), (3, 1), (1, -4)}.