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Greatest integer function with linear function inside

Amer

Active member
Mar 1, 2012
275
What is the best way to redefine Greatest integer function as a piecewise function for example

f(x) = [ 2x - 3 ] , -2<= x <= 1
 

dwsmith

Well-known member
Feb 1, 2012
1,673
What is the best way to redefine Greatest integer function as a piecewise function for example

f(x) = [ 2x - 3 ] , -2<= x <= 1
If my memory service me correctly, you should be able to write it as
$$
f(x) = [2x] - 3
$$
At -2, you have -7.
(-2,-3/2), you have -6.
(-3/2,-1) -5
At -1, you have -5
(-1,-1/2) -4
etc
After writing all that out, you should be able to develop a piecewise function.
 

Amer

Active member
Mar 1, 2012
275
Thanks, since I am a teacher i was looking for the easiest way to redefine it as a piecewise function.