Why matlab gives graph of exp(1/x) and exp(-1/x) wrong?

when trying to find graph of exp(1/x) and exp(-1/x) i am getting graphs that definitely not belong to exp(1/x) and exp(-1/x).

my codes are:

syms x
y=exp(-1/x) % or y=exp(1/x)
fplot(y)

when i run this, i get the graphs that as in below, figure 1 is belong to exp(-1/x) and figure 2 is belong to exp(1/x)

figure 1=exp(-1/x)

figure 2=exp(1/x)

But, this is absolutely ridiculous. The graphs of exp(1/x) and exp(-1/x) must be like :

Is there anybody that will help me? I do not know where i am wrong, please if you know help me

thanks

Answer 1

[Stephen23]

fun = @(x) exp(-1./x);
fplot(fun)
ylim([0,10])

fun = @(x) exp(1./x);
fplot(fun)
ylim([0,10])

I doubt there is much that can be done to change the automatic discontinuity detection algorithm, but feel free to read the documentation and see.

[ali yaman]

Firs of all, i thanx to you for your respond.

But, could you explain me that why i need to write like your code, what is difference between mine and yours code.

Also, why there is need to indicate limitations, like ylim([0,10]). Besause when i run your code without ylim([0,10]) it gives me wrong graph, but when write it gives correct.

[Stephen23]

"what is difference between mine and yours code."

• changed symbolic code into a normal MATLAB function (optional)
• added Y-limits (required to see only the part of the function you want)

"it gives me wrong graph, but when write it gives correct."

Actually both of the graphs are perfectly correct. Perhaps this is the first time you have seen that function plotted with very large Y-limits, but suffice to say, but that is exactly how it looks like. What do you expect to be plotted if those function values are very very large? (hint: fplot plots very very large values, just as the Y-axes show). If you only want to see a part of the plot (and not all of those very very large function values) then you can simply restrict the axes Y-limits.

[ali yaman]

"What do you expect to be plotted if those function values are very very large?"

yes dear @Stephen Cobeldick you are right.

But, what if i do not know the function has very very large on y-axis, also what if i do not know asymptote of the function (in my example asymptotes are 1); in these cases how i do know where i should take as limitations ?

For example: if i want to plot graph of y= exp(cos(x))-x^2+5/x

in this case neither i nor you we do not know where is asymptote of the function and wheter the function has large value on y-axes, thus we do not know where we should take as limits. Now, how can we decide the limitations, to get a correct shape of curve? What do you prefer? do u have any idea?

Thanks

By the way sorry for my poor english, i hope that i expressed myself :)

[Stephen23]

"Now, how can we decide the limitations, to get a correct shape of curve?"

The shape is always "correct", as explained above. The only difference is how humans like to focus on particular parts or features of the curve: the computer does not know which parts you are interested in, only you know that. Possibly someone has published a heuristic algorithm to predict Y-limits for arbitrary functions.

[ali yaman]

Dear @Stephen Cobeldick thanx for all your answer, i got it.

i can't thank you enough!