Answer:
A function that changes the same way can be a linear function.
y = a*x + b.
Where the rate of change (this is, how much changes y when x increases or decreases) is defined by the coefficient a, that is constant.
for example, suppose that when x = x0, we have y = y0
y0 = a*x0 + b.
Now x0 increases by one unit, to (x0 + 1)
y = a*(x0 + 1) + b = (a*x0 + b) + a = y0 + a.
Then if x increases (or decreases) 1 unit, y increases (or decreases) a units.
Now, we can define the rate of change of a function as it's derivate with respect to some variable.
In this case, if we derive with respect to x, we have:
y' = a
Then the rate of change is constant.