Greatest integer function with linear function inside

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SUMMARY

The Greatest Integer Function (GIF) can be redefined as a piecewise function using linear expressions. For the function f(x) = [2x - 3] within the interval -2 <= x <= 1, it can be expressed as f(x) = [2x] - 3. This formulation allows for the calculation of specific values at defined intervals, such as f(-2) = -7 and f(-1) = -5. The discussion emphasizes the importance of clearly outlining the piecewise segments to facilitate understanding and teaching.

PREREQUISITES
  • Understanding of the Greatest Integer Function (GIF)
  • Familiarity with piecewise functions
  • Basic knowledge of linear functions
  • Ability to evaluate functions at specific intervals
NEXT STEPS
  • Research how to construct piecewise functions in mathematical notation
  • Learn about the properties and applications of the Greatest Integer Function
  • Explore linear function transformations and their graphical representations
  • Study examples of piecewise functions in calculus and their applications
USEFUL FOR

Mathematics educators, students studying piecewise functions, and anyone interested in the applications of the Greatest Integer Function in mathematical analysis.

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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