MHB Greatest integer function with linear function inside

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The discussion focuses on redefining the Greatest Integer Function (GIF) as a piecewise function, specifically for f(x) = [2x - 3] within the interval -2 <= x <= 1. A suggested approach is to express it as f(x) = [2x] - 3, which allows for easier computation of values at specific points. The values calculated at key intervals, such as -2 and -1, help outline the behavior of the function. The conversation emphasizes the importance of clarity and simplicity in teaching this concept. Overall, the goal is to create an accessible piecewise representation for educational purposes.
Amer
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What is the best way to redefine Greatest integer function as a piecewise function for example

f(x) = [ 2x - 3 ] , -2<= x <= 1
 
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Amer said:
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.
 
Thanks, since I am a teacher i was looking for the easiest way to redefine it as a piecewise function.
 

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