Question

Which of the following tables represents a function? a x 4 4 9 9 y 2 −2 3 −3 b x 2 −2 3 −3 y 4 4 9 −9 c x 1 −1 1 −1 y 4 5 6 7 d x 5 5 6 6 y 1 2 3 4

Answer 1

Table b is the only table that represents a function because each x-value is paired with exactly one y-value, which is a requirement for a function.

Step-by-step explanation:

To determine which of the given tables represents a function, we use the definition that a function assigns exactly one output (y-value) for each input (x-value). Here are the tables analyzed:

• Table a: x-values of 4 and 9 are each paired with two different y-values, so this is not a function.
• Table b: All x-values are associated with distinct y-values, even though the y-values repeat, this is still a function because no single x-value is paired with multiple y-values.
• Table c: x-values of 1 and -1 are each paired with two different y-values, so this is not a function.
• Table d: x-values of 5 and 6 are each paired with two different y-values, so this is not a function.

The table that represents a function is table c. In this table, each value of x corresponds to a unique value of y. For example, when x is 1, y is 4. When x is -1, y is 5. This one-to-one relationship between x and y is what defines a function.

Therefore, table b is the only table that represents a function due to the dependence of y on x.