The correct statement is option B: The mapping represents y as a function of x, because each y-value corresponds to exactly one x-value.
The mapping represents y as a function of x, because each y-value corresponds to exactly one x-value.
In a mapping, the x-values are paired with the corresponding y-values. For it to represent y as a function of x, each x-value must have only one corresponding y-value. This means that every input (x-value) in the mapping has a unique output (y-value). In option B, it states that each y-value corresponds to exactly one x-value, which indicates that the mapping represents y as a function of x.
Let's consider an example to further illustrate this concept. Suppose we have the mapping:
x: 1 2 3 4
y: 2 4 6 8
In this mapping, each x-value has a unique corresponding y-value. For example, when x is 1, y is 2; when x is 2, y is 4; and so on. Therefore, this mapping represents y as a function of x.
On the other hand, option A states that the mapping does not represent y as a function of x because two of the x-values correspond to the same y-value. In a function, each input (x-value) should have a unique output (y-value), so if two different x-values have the same y-value, it violates the definition of a function.
Options C and D also discuss the number of x-values and y-values in the mapping. However, the key factor in determining if the mapping represents y as a function of x is whether each x-value has only one corresponding y-value, as stated in option B.