In mathematics, a constant function is one defined in which a function whose output value (y) is the same for every value of the input variable (x). Therefore this means that whatever is the value for x, the value of y would always be the same. Hence we can say that the function is a straight horizontal line in a Cartesian plane.
Since the value of y does not change, and the average rate of change has the formula:
average rate of change = (y2 – y1) / (x2 – x1)
So y2 – y1 = 0 therefore average rate of change is also zero.
Hence to complete the sentence:
For a constant function, the y-coordinate is the same for every pair of points selected, so the average rate of change always has a value equal to zero.