Question

which relation is a function?
a. {(1,2),(3,1),(4,2),(7,2)}
b. {(1,2),(1,3),(4,5),(6,1)}
c. {(0,1),(1,2),(0,2),(2,3)}
d. {(1,4),(1,5),(2,4),(3,6)}
e. {(2,4),(2,5),(2,6),(2,7)}

Explanation:

Step1: Recall function definition

A relation is a function if every input (x-value) has exactly one output (y-value).

Step2: Check Option A

All x-values: 1, 3, 4, 7. Each x has only one y.

Step3: Check Option B

x-value 1 maps to 2 and 3. Not a function.

Step4: Check Option C

x-value 0 maps to 1 and 2. Not a function.

Step5: Check Option D

x-value 1 maps to 4 and 5. Not a function.

Step6: Check Option E

x-value 2 maps to 4,5,6,7. Not a function.

Answer:

A. {(1,2), (3,1), (4,2), (7,2)}