Question

Which of the relations does NOT represent a function?

a) {(-9, 8), (-2, 14), (7, -2), (9, 3), (0, 4)}
b) {(-3, 2), (4, 6), (6, 2), (-1, 5), (3, -1)}
c) {(-3, 4), (6, 1), (-6, -9), (10, -2), (-3, -1)}
d) {(-5, -5), (4, 3), (-7, -2), (0, -5), (9, 12)}

Answer 1

A relation represents a function if each input value is associated with exactly one output value. The relation that does NOT represent a function is c) {(-3, 4), (6, 1), (-6, -9), (10, -2), (-3, -1)}.

Step-by-step explanation:

A relation represents a function if each input value (x) is associated with exactly one output value (y). To determine which of the given relations does NOT represent a function, we need to check if there are any repeated x-values. If there are, then it is not a function.

Let's analyze each relation:

1. Relation a) has distinct x-values, so it represents a function.
2. Relation b) has distinct x-values, so it represents a function.
3. Relation c) has repeated x-value (-3), so it does NOT represent a function.
4. Relation d) has distinct x-values, so it represents a function.

Therefore, the relation that does NOT represent a function is c) {(-3, 4), (6, 1), (-6, -9), (10, -2), (-3, -1)}.