Sunday, November 4, 2012

Mathematica Plot: Plotting More than One Function

Using Plot to Plot More than One Function

It is often useful to Plot different function parameter values and compare them. Just give Plot a list of functions with the parameter values you wish to compare and it will Plot them together without your having to use Show. Let us use the function defined in Basic Plotting:

f[x_, t_] := x^t;

You can use Table to automate the parameter sweep, but pre-generate the sweep functions or (for reasons I don't understand) Plot won't automatically color-code them.

In[278]:= sweepFunctionTable = Table[f[x, t], {x, 2, 5}]

Out[278]= {2^t, 3^t, 4^t, 5^t}

In[279]:= Plot[sweepFunctionTable, {t, 0, 5}]

Plot with Tooltip to Identify the Plots

Sometimes you can lose track of which function is which when plotting several function together. Plot helps by color-coding them. But adding Tooltip labels is another technique. Let's compare the three functions Sin x, Cos x, and Sin x + Cos x. You will need to Plot this yourself in a Notebook to mouseover and see the tooltips that label each curve with the three function names ("Sin@x", "Cos@x", "Cos@x + Sin@x").

Plot[Tooltip@{Sin@x, Cos@x, Cos@x + Sin@x}, {x, -3 Pi, 3 Pi}]

Now let's specify that the tick marks should be labeled in radians:

Plot[Tooltip@{Sin@x, Cos@x, Cos@x + Sin@x}, {x, -3 Pi, 3 Pi},
 Ticks -> {{-3 Pi, -2 Pi, -Pi, 0, Pi, 2 Pi, 3 Pi}, Automatic}]

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