How Do You Graph the Function f(x) = x - [[x]]?

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SUMMARY

The function f(x) = x - [[x]] can be graphed by understanding that [[x]] represents the floor function, denoted as [x]. To visualize this function, one should calculate specific values at points such as 0.5, 0.7, 0.9, 1.2, 1.4, 1.7, 2.5, 2.7, and 2.9. The resulting graph will illustrate the behavior of f(x) as it oscillates between integer values, confirming that the graphing process is straightforward once the definition of [[x]] is clarified.

PREREQUISITES
  • Understanding of the floor function, denoted as [x]
  • Basic knowledge of graphing functions
  • Familiarity with evaluating functions at specific points
  • Ability to interpret graphical representations of mathematical functions
NEXT STEPS
  • Learn how to graph piecewise functions
  • Explore the properties of the floor function in depth
  • Investigate the implications of discontinuities in functions
  • Practice plotting various functions using graphing software like Desmos
USEFUL FOR

Mathematics students, educators, and anyone interested in understanding and graphing piecewise functions, particularly those involving the floor function.

brhum
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How do you graph f(x) = x - [[x]]
 
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Well that will depend upon what "[[x]]" means! If it is the "floor" function, you should be able to calculate a few values at, say 0.5, 0.7, 0.9, 1.2, 1.4, 1.7, 2.5. 2.7, 2.9 and see for your self.
 
brhum said:
How do you graph f(x) = x - [[x]]

Do you see that [[x]] is same as [x]? Plotting f(x) should be trivial once you notice that.

(assuming [x] denotes the floor function)
 

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