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)}
The correct answer is d) {(1, 12), (2, 8), (3, 1), (1, -4)}.
A function can only have one unique output (y-value) for each input (x-value). In option d), we have two different outputs for the same input value of 1, namely 12 and -4. This violates the definition of a function, so d) does not represent a function.
To determine which of the given options does not represent a function, we need to verify if each option satisfies the criteria for a function.
A function is a relation between two sets where each element of the first set (called the domain) is associated with exactly one element of the second set (called the range).
Let's analyze each option:
a) {(1, 3), (2, 5), (5, 3), (7, 10)}:
- In this case, each element in the domain has a unique mapping to an element in the range. Therefore, option a) represents a function.
b) {(-1, 4), (2, 4), (0, 4), (9, 4)}:
- Similarly to option a), each element in the domain has a unique mapping to an element in the range. Therefore, option b) represents a function.
c) {(-3, -2). (-1, 0), (3, 7), (6, 1)}:
- Upon closer inspection, we can see that (-3, -2) and (-1, 0) have the same x-value in the domain, but different y-values in the range. This violates the definition of a function since the same input is associated with multiple outputs. Therefore, option c) does not represent a function.
d) {(1, 12), (2, 8), (3, 1), (1, -4)}:
- In this case, we see that (1, 12) and (1, -4) have the same x-value in the domain, but different y-values in the range. Similar to option c), this violates the definition of a function since the same input is associated with multiple outputs. Therefore, option d) does not represent a function.
Based on the analysis, the option that does NOT represent a function is c) {(-3, -2). (-1, 0), (3, 7), (6, 1)}.