does anyone think that there are any other types of functions that have the same rate of change over every interval?
Stacey Warren - Expert brainly.com
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you mean two different functions that have the same derivative?
like how linear equations have the same rate of change everywhere on the graph, are there other graphs that are like that?
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
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does it f(x)=|x| count as a linear graph?
What about y = e ^ x?
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.
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
f(x)=|x| is also considered a linear equation
right, but it has a different rate change over x<0 than from x>0 so I excluded it from possibility