Quick question about probability function?

Question

Say f(x) = |x| is a density function with domain [-1,1] and 0 elsewhere.

When sketching the function, does the 0 (elsewhere) line have a domain of (-infinity, -1) and (1, infinity) or (-infinity, -1] and [1, infinity) ?

If (-infinity, -1] and [1, infinity), why is this so?

I hope my description is clear :( Thanks a lot for any help.

Answer 1

f(x) = |x| has a natural domain of all the Real numbers or - infinity to infinity.

The probability function removes from the natural domain a subset [-1, 1] and assigns the range 0 to all numbers outside the small interval the answer 0.

so the graph needs to reflect this over the three intervals:

The graph of the function (- infinity, -1) will be 0 [-1, 1] will be |x| and finally, 91, infinity will be 0.

Answer 2

I don't think that the function exists outside the domain given.  Otherwise all functions would be from -infinity to + infinity).  You see when you say "sketching the function" then it does not exist outside the domain given. I think the convention is that you have closed dots at the end of the graphs.

Also the mod x means the lines are above the X axis Like a capital V.