Putting "forbidden values" for functions

Question

I am defining a function $f(x)$ and I would like to put undefined values to some $x$. The point is that if I plot the function I don't want an error to be returned, I want that for all the plotting function I will use, it will "ignore" the $x$ corresponding to forbidden values.

Is there a simple way to do this (i.e not writing 50 lines of functions). Is there a simple keyword for that ?

Answer 1

I thought that Plot ignored values that are not numbers and also suppressed errors. When I try the following:

f[x_?(2 <= # <= 4 &)] := 1/0;
f[x_?(4 < # <= 6 &)] := Indeterminate;
f[x_] := x^2;

and then

Plot[f[x],{x,0,10}]

I don't get any errors and the plot ignores x values from 2 to 6.

Answer 2

There are two issues here:

Defining the function

You could use a Condition to prevent the function from evaluating at the forbidden points:

forbiddenValues = {1, E, Pi};
forbiddenQ[x_] := Or @@ Table[x == value, {value, forbiddenValues}] // Evaluate;
f[x_] /; !forbiddenQ[x] := x^2

f /@ {1, 2, E, 4, Pi}
(* {f[1], 4, f[E], 16, f[Pi]} *)

Plotting

From @Natas's comment, use Exclusions:

Plot[f[x], {x, 0, 5}
  , Exclusions -> forbiddenValues
  , ExclusionsStyle -> {None, Directive[Red, PointSize[Large]]}
]

Despite the definition above, you still need to explicitly specify the locations of the exclusions because they do not get detected automatically. Therefore, if the only goal is to generate a plot with the exclusions, I would not bother with defining the function above. Just plot x^2 and use the appropriate exclusion options.