Question

Which of the following tables represents a function?

a. x 3 3 4 4
y 2 2 3 3

b. x 5 5 5 5
y 2 2 8 8

c. x 3 3 5 5
y 4 5 6 7

d. x 4 4 5 5
y 2 2 3 3

Answer 1

Tables a and d represent functions because each x-value corresponds to exactly one y-value, fulfilling the definition of a function. Tables b and c do not represent functions because they assign multiple y-values to single x-values.

Step-by-step explanation:

To determine which table represents a function, we must remember the definition of a function in mathematics: each input value (x) must be paired with exactly one output value (y). A function cannot assign multiple outputs to a single input. Let's examine each table provided against this definition.

• Table a: This table shows that the input value 3 corresponds to the output value 2, and the input value 4 corresponds to the output value 3. Since each x-value has one unique y-value, this table represents a function.
• Table b: This table shows that the input value 5 corresponds to two different output values: 2 and 8. This violates the definition of a function, so table b does not represent a function.
• Table c: Similarly to table b, the input value 3 corresponds to two different output values: 4 and 5. Thus, table c does not represent a function.
• Table d: This table behaves like table a, in that each x-value is paired with exactly one y-value. Therefore, table d represents a function.

Given the definitions and the tables provided, only tables a and d satisfy the requirement of a function. A function must map each distinct input x to exactly one output y, which both tables a and d do correctly. Therefore, tables a and d represent functions.