If you are interested in seeing a display of y=f(x), over a real interval 0<=x<=10, say, and where f is real-valued, finite, continuous, etc. on that interval, there are many programs that are available to help.
What if f is real-valued (etc.) but the program that you use to compute f has some round-off error that results in small imaginary parts? How might you deal with this as a policy in a plotting program?
Some possibilities that come to (my) mind:
1. Instead of plotting f(x), plot realpart(f(x)), perhaps making some kind of warning noise. This assumes imagpart(f(x)) is smaller than some ignorable relative quantity compared to realpart. (difficulty: what if realpart is small too???). 1b. (Same as 1 except no warning)
2. Leave blank spots on the display where the values of f(x) are not purely real. 2b. (Same as 2 except issue warnings)
This should only be an issue if f(x) is computed by some formula that you have concocted.
If f(x) is a good library function f:Real->Real, it should not product results with non-zero imaginary components.
This problem came up in plotting, in Mathematica 7, this function:
JacobiSN[x,3] which is real for 3<x<5, yet a plot of it shows a gap around 4.
If you have Mathematica available, you can see the result from executing this: