Question

A function that changes in the same way all the time is?

Answer 1

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.