Can a graph have a horizontal asymptote and have an inflection point?

[nsodf]

I've tried to create this type of function but can't seem to create an equation with both

 

[MarkFL]

Yes, an example that springs to mind is the standard normal distribution. Here is a plot showing the points of inflection:



[MATH]y=\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}[/MATH]
The $x$-axis is the horizontal asymptote.

 

[Dr.Peterson]

If you are looking for a rational function, you can make one that looks very similar to this.

 

[topsquark]

Hydrogen probability functions are fun, too.

This is the 2s state of Hydrogen. $$R(r) = r^2 (2 - r )^2 e^{-r}$$. (I've set $$a_0 = 1$$ for clarity.) Ignore the -x part.


-Dan

 

[nsodf]

Can you give an example of a rational function?

 

[MarkFL]

Can you give an example of a rational function?

Try:

[MATH]f(x)=\frac{1}{x^2+1}[/MATH]