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Think of a line graph where the line stays somewhat flat and low to the ground for a while (but still upsloping, nondecreasing) and then starts to arc up.

I'm trying to figure out a way to "characterize" these kinds of lines (when does this "hard arc" point occur, how hard is the arc, etc). Please ask questions if I am not being clear.

I tried to draw an example of what I mean https://i.stack.imgur.com/Z7HWe.png

For example I should be able to have a model equation that describes a line like this, and based on whatever such coefficient I can say "This coefficient means the arc starts to occur sooner" or "This coefficient means the arc, when it occurs, is rather strong." Does this make sense?

A.S
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Nakano
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1 Answers1

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These are graphs of $e^x$. You can see at x=0 the graph starts raising and after 10 it's just increases drastically like a vertical line.

So, for $Ae^{x-c}$ the graph will start shooting upwards at $x-c=0$ C shifts graph from one place to other on X-axis.

and the A controls the amplitude of the function and B controls the argument of function $f(x)$ , so it can even reverse the whole curve too (b<0).

ABC
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  • http://www.wolframalpha.com/ Enter any function here and see every here and there of it. – ABC Apr 04 '13 at 03:40