does anyone think that there are any other types of functions that have the same rate of change over every interval?

Question

turingtest · Answer

you mean two different functions that have the same derivative?

anonymous · Answer

like how linear equations have the same rate of change everywhere on the graph, are there other graphs that are like that?

turingtest · Answer

if the graph is curvy then it does not have a constant rate of change in cartesian coordinates, so yes it must be a straight line

anonymous · Answer

does it f(x)=|x| count as a linear graph?

directrix · Answer

What about y = e ^ x?

turingtest · Answer

I was interpreting 'a constant rate change' here to mean that the graph has a constant first derivative everywhere. f(x)=|x| does not have f'(0) defined, and y=e^x has a variable first derivative. 
I think the problem is a bit vague though.

anonymous · Answer

ya i just said that i didnt because in order to have the same average rate of change over every interval  you need a straight line and by definition that is unique to linear equation

anonymous · Answer

f(x)=|x| is also considered a linear equation

turingtest · Answer

right, but it has a different rate change over x<0 than from x>0 so I excluded it from possibility

turingtest · Answer

plus it's rate of change is not defined at zero