Q: Draw the graph of the function: f(x) = x - [x] for all x belongs to [-3, 3]  Note: i) Please explain the all steps with Graph ii) Its a Saw-tooth Wave function or Fractional Part Function

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Graph `f(x)=x-[x]` ** [x] is the floor function` ` or greatest integer function. [x] is the greatest integer that is not larger than x.

Ex: [1.5]=1;[1.99997]=1;[.2]=0,[-.5]=-1;[3]=3

The graph:

The open dots at the end of each segment are exaggerated. Many graphing utilities will connect the graph, but this is incorrect.

Some points:

x| -2 -1.75 -1.5 -1.25 -1 -.75 -.5 -.25 0 .25 .75 1 1.5 2 2.3 3 3.1
y|  0 .25     .5     .75   0    .25  .5   .75 0 .25 .75 1 .5 2   .3   3  .1

f(-1.25)=-1.25-[-1.25]=-1.25-(-2)=.75

f(-.5)=-.5-[-.5]=-.5-(-1)=.5

f(3.1)=3.1-[3.1]=3.1-3=.1

f(2)=2-[2]=2-2=0

** You must be careful with graphing utilities -- the greatest integer function is not the round function -- this rounds to the nearest integer. It is also not the integer part function (ipart) -- this works for positive numbers (truncates the decimals) but does not work for negative numbers.

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