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anonymous

  • 4 years ago

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

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  1. TuringTest
    • 4 years ago
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    you mean two different functions that have the same derivative?

  2. anonymous
    • 4 years ago
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    like how linear equations have the same rate of change everywhere on the graph, are there other graphs that are like that?

  3. TuringTest
    • 4 years ago
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    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

  4. anonymous
    • 4 years ago
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    does it f(x)=|x| count as a linear graph?

  5. Directrix
    • 4 years ago
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    What about y = e ^ x?

  6. TuringTest
    • 4 years ago
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    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.

  7. anonymous
    • 4 years ago
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    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

  8. anonymous
    • 4 years ago
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    f(x)=|x| is also considered a linear equation

  9. TuringTest
    • 4 years ago
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    right, but it has a different rate change over x<0 than from x>0 so I excluded it from possibility

  10. TuringTest
    • 4 years ago
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    plus it's rate of change is not defined at zero

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