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Let's try a box with some numbers in it:

THE RULE:  Add 1

input  ->  rule: +1  ->  output
 

What can we put in this box?

input: 3  ->  rule: + 1  ->  output: 4  ...  input: pi  ->  rule: + 1  ->  output: pi + 1
 

We can put anything in this box -- even goofy irrational numbers like pi!  So...

domain  =  all real numbers

   range  =  all real numbers