Which function represents the reciprocal of x?

The function that represents the reciprocal of x is defined as a function that outputs the value of 1 divided by the input value x. This function can be mathematically expressed as y = 1/x, which means that for any input value x (except for x = 0, where the function is undefined), the output will be the reciprocal of x.

For example, if x = 2, then y = 1/2, and if x = -3, then y = 1/(-3) = -1/3. This behavior is characteristic of the reciprocal function and thus makes it distinct.

This is why the answer y = 1/x is the correct representation of the reciprocal of x. Functions that involve negative signs, such as y = -1/x, represent the negative reciprocal, which behaves differently. Meanwhile, y = x and y = x² do not represent any reciprocal relationship; they indicate direct proportionality and quadratic relationships, respectively.