Creating lung compliance curves but I'm terrible at the math/graphing

sozme
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Homework Statement



I am trying to replicate the curves in the attachment, but since I am a physiologist it has been quite a while since I've done graphing. I am simply looking for an easy way to replicate these three curves. This is for a practice exam I am creating for first year medical students. The graphing program I got from sourceforge allows you to create these curves by inserting a function in the form of f(x) = or creating a point series.

Homework Equations



I believe the normal curve is roughly f(x) = √x but, I wish I knew what function to insert to make the line cross the X axis at +2.5 instead of 0. I am clueless how to create the shapes of the other two.

The Attempt at a Solution



Above
 
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sozme said:

Homework Statement



I am trying to replicate the curves in the attachment, but since I am a physiologist it has been quite a while since I've done graphing. I am simply looking for an easy way to replicate these three curves. This is for a practice exam I am creating for first year medical students. The graphing program I got from sourceforge allows you to create these curves by inserting a function in the form of f(x) = or creating a point series.

Homework Equations



I believe the normal curve is roughly f(x) = √x but, I wish I knew what function to insert to make the line cross the X axis at +2.5 instead of 0. I am clueless how to create the shapes of the other two.

The Attempt at a Solution



Above

I don't see an attachment -- try again?
 
If your curve has the same shape as f(x) =√x, it can be translated to the right by 2.5 units to have an x-intercept at (2.5, 0). That would be y = f(x - 2.5) = √(x - 2.5)
 
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berkeman said:
I don't see an attachment -- try again?

I'm sorry, I think it should be attached now. Thanks for that first answer Mark. Now the other 2 curves should be in the attachment and I need a way to recreate them.
 

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  • lungcompliance.jpg
    lungcompliance.jpg
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Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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