Question

does this table represent a function? why or why not?
a. yes, because every x - value corresponds to exactly one y - value.
b. yes, because there are different y - values.
c. no, because one x - value corresponds to two different y - values.
d. no, because the y - values are positive.

Explanation:

Step1: Recall the definition of a function

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

Step2: Analyze the given table

Looking at the x - values: The x - value of 3 appears twice. When \(x = 3\), in one case \(y=4\) and in another case \(y = 3\). So, the x - value 3 is associated with two different y - values. Since a function requires that each x - value has exactly one y - value, this table does not represent a function because one x - value (x = 3) corresponds to two different y - values.

Answer:

C. No, because one x - value corresponds to two different y - values.