Question

Which relation is not a function?

a) {(8,16), (9,18), (10,20), (11,21), (12,24)}
b) {(-10,100),(-5,25), (-2,4), (0,0), (2,4)}
c) {(4,2), (16,4), (17, 17), (25,5), (36,6)}
d) {(-1, -1), (-1,1),(0,0), (3, –3), (4, -4)

Answer 1

Relation d) is not a function because it assigns two different outputs to the same input of -1, which violates the definition of a function.

Step-by-step explanation:

To determine which relation is not a function, we look for any instance in which an input (or x-value) has more than one output (or y-value). A function must have exactly one output for each input.

• Relation a) – All inputs have different outputs.
• Relation b) – All inputs have different outputs.
• Relation c) – All inputs have different outputs.
• Relation d) – The input -1 has two different outputs (-1 and 1), which means this relation is not a function.

Therefore, the correct answer is d) {(-1, -1), (-1,1), (0,0), (3, –3), (4, -4)} because the same input of -1 produces two different outputs.

Answer 2

Relation d) {(-1, -1), (-1,1),(0,0), (3, –3), (4, -4)} is not a function because it maps the same x-value (-1) to two different y-values (-1 and 1), violating the definition of a function.

Step-by-step explanation:

To determine which relation is not a function, we need to look at the pairs of numbers in each relation and check for uniqueness of the x-values (the first number in each pair). A function must associate each input with exactly one output, which means for each x-value there must only be one y-value.

Relation a) {(8,16), (9,18), (10,20), (11,21), (12,24)} is a function because all x-values are unique.

Relation b) {(-10,100),(-5,25), (-2,4), (0,0), (2,4)} is a function as well, despite the y-value 4 repeating, because it is associated with different x-values.

Relation c) {(4,2), (16,4), (17, 17), (25,5), (36,6)} is also a function since each x-value is unique.

Relation d) {(-1, -1), (-1,1),(0,0), (3, –3), (4, -4)} is not a function because the x-value -1 is associated with two different y-values (-1 and 1). This violates the definition of a function.