How to Break Graphing Applications

Graphing applications seem appear to magically draw any graph you throw at them. But as with any automated tools, it is necessary to know their limitations. In this blog, we will discuss various ways in which we can test the limits of a graphing application and how to use them for the best results.

It is difficult for graphing applications to draw graphs with large number of branches. One example of it is $y=tan(xy)$. If we graph this function with GraphOE, we get the following graph:

Plot of y=tan(xy)

We can clearly see that the equation has lots of branches. These kind of branches are more likely to be present when we use trigonometric functions like $\sin,\tan,\cos$ etc.

Implicit Functions

Implicit functions are functions of form $f(x,y)=0$. For example, $f(x,y)=x^2+y^2-1=0$ is an equation of a circle. In general, it is time-consuming and harder to plot implicit functions. If we have some trigonometric functions in implicit equations then we are likely to encounter missing details. The best way to get higher details is to zoom in about the region of interest. Graphing applications will fall back to lower details when encountered with large number of branches.

Get the Best Plots

Some suggestions to get the best plots listed as follows:

1. Use view port around $x=(-10, 10)$ and $y=(-10, 10)$. Don't use very small view ports or very large view ports.
2. Place graphs near to the origin.
3. Scale the graph whenever possible.
4. Don't use large coefficients for input to trigonometric functions. Eg: $y=sin(100000x)$ will not be plotted with all the details.