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This is graph of function `f(x)=[x-2] +2` that has zero for `-1 <= x <= 0`
the set of definition and the range of this function is `RR`
Note , if we divide the set of definition in open intervall `I_n=(n; n+1)` with `n` integer, `AA x in I_n` `f'(x)=0`
This means all around set of definition `f(x) ` derivative zero. even tought function isn't costant.
(This is the clear test against of assertion: "a funcion with derivative zero all its define set zero is costant")
Given y=[x-1]+2 (Assuming [x] is the greatest intger function):
The greatest integer function returns the greatest integer that is less than or equal to the given input.
For values of x>0 [x] is just the integer part of the number (also called the truncate function or integer function.) e.g. [1.6]=1
For values of x<0 [x] is the integer part minus 1. e.g. [-1.3]=-2
Take the graph of [x], shift it 1 unit to the right and two units up.
The graph of [x] in red, [x-1] in blue, and [x-1]+2 in green:
In tabular form:
`-5<=x<-4 ` y=-4
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