Question

Is the relation a function?Select Yes or No for each relation

a. (3, 3) (3, -2) (-2, 4) and (1, -6)
b. (3, 3) (5, -2) (-2, 4) and (1, -2)
c. (3, 3) (5, -2) (-2, 4) and (5, 9)
d. (3, 3) (5, -2) (-2, 4) and (4, 9)

Answer 1

A relation is a function if each input is paired with only one output.

a. No

b. Yes

c. No

d. Yes

Step-by-step explanation:

To determine if a relation is a function, every input (x-value) of the relation must correspond to exactly one output (y-value). If an x-value is paired with multiple y-values, the relation is not a function.

1. For relation a: (3, 3) (3, -2) (-2, 4) (1, -6). Here, the x-value 3 corresponds to two different y-values (3 and -2), so this relation is not a function.
2. For relation b: (3, 3) (5, -2) (-2, 4) (1, -2). All x-values are unique and paired with only one y-value, which makes this a function.
3. For relation c: (3, 3) (5, -2) (-2, 4) (5, 9). The x-value 5 has two different y-values (-2 and 9), so this is not a function.
4. For relation d: (3, 3) (5, -2) (-2, 4) (4, 9). All x-values are unique and each paired with only one y-value, hence this relation is a function.

Therefore, the correct options are:

• a. No
• b. Yes
• c. No
• d. Yes