# What software that properly calculate asymptote?

I am pretty sure I can ask about software that mathematicians use.

I have been exploring offline and online software to make a simple graph :

$$y=3^x - 1$$

However most of them crossed the asymptotes when it isn't supposed to. because $y\ne -1$. If $-1=3^x - 1$, then $3^x=0$, which is never true.

So when I generate the graph, it will always result in some points to be $y=-1$.

So which software(s) that can properly avoid cutting asymptote $(y=-1)$

Software I have tried:

1. Microsoft Mathematics

2. Some cheapo online tools that come first in google search(es).

3. Famous online graphing tool, Desmos, which gives an unwanted result:

• Try DESMOS to see – imranfat Sep 23 '16 at 13:53
• i come from AnimeSE so I am not aware of good softwares and how these programs return the value y=-1 when it clearly impossible, so I came here asking for help – LordSacha Sep 23 '16 at 14:01
• and I am very sorry for asking silly question. but I need the thing that shows the lil bit floating and doesnt return the value y=-1 in the curve. – LordSacha Sep 23 '16 at 14:02
• Alright, a better program might show $-0.99993876223655202351234512322670332340$ as approximation for $3^{-8.83}-1$. So what you want is arbitrary precision arithmetic in a grpahińg tool that is obtained by interpolating a limited number of points anyway? – Hagen von Eitzen Sep 23 '16 at 14:06
• Ask yourself how you would draw this on a sheet of paper, and up to what point you would be able to separate the curve from the asymptote. A piece of software is no magick, it will have to plot on pixels, almost the same way you draw on paper. What do you expect? – Jean-Claude Arbaut Sep 23 '16 at 14:14

The number $3^{-8.83}-1$ is within $6\times 10^{-5}$ of $-1$. The scale of your image looks like about $1$ centimeter per unit. So to separate the graph of the function from the asymptote, a resolution on the other of $10{,}000$ pixels per centimeter, or $25{,}400$ pixels per inch, is necessary.

Wikipedia says the spatial resolution of standard computer monitors is $72$–$100$ pixels per inch.

• that is a very fine explanation. I can add that as part of 'explanation' for my (silly) teacher who rejects both my non-proportional graph and my proportional graph that cuts 'the almighty' asymptote. Also thank you for helping the future mathematician. – LordSacha Sep 23 '16 at 14:32

I need the thing that shows the lil bit floating and doesnt return the value y=-1 in the curve.

If all you want is the picture to make your point, consider asking the software not to show the point $(-8.83, -1)$ as the red dot, or edit it out in a tool like photoshop. Then your reader will see the graph overlaying the axis (because it's so close) and the little uptick at the end and not be confused.

• It is a nice suggestion to trick the eye of my teacher, but Matthew's explanation proves that it is improbable to achieve (or visible in the naked eye) a result that is not y=-1 in a normal screen or even printer... – LordSacha Sep 23 '16 at 14:29

The idea of vector graphics is that if you zoom in on an image, you continue to get the best image your monitor can display (or the best your printer can print), unlike raster graphics where you just get bigger dots.

Using a graphing tool such as Desmos, you can zoom in on any particular part of your graph in order to see fine details such as the very tiny separation between the graphs of $y=3^x - 1$ and $y = -1$ at $x = -8.83$. Here's an image of Desmos.com zoomed in on that section of the graph:

The distance between the thick lines is $0.001$ in this figure (see the coordinates along the top and left edges of the figure) and the distance between the thin lines is $0.0002$. The origin $(0,0)$ would be a very large distance to the upper right if we had a large enough screen to show it on.

The downside of zooming in like this is that you can't see the general shape of the graph, since you are looking at such a tiny portion of it. To better visualize the graph you might want to look at several screenshots at different zoom levels.