For all define

where denotes the greatest integer less than or equal to . Draw the function for each of the following on the interval :

- .
- .
- .
- Graph of .
- Graph of .
- The graph of .
- The graph of .

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Stumbling Robot

A Fraction of a Dot
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Tag: Step Functions

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Draw the graphs of some step functions

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Draw graphs of some step functions

For all define

where denotes the greatest integer less than or equal to . Draw the function for each of the following on the interval :

- .
- .
- .
- Graph of .
- Graph of .
- The graph of .
- The graph of .

Define a function

(The function is not defined if or .)

- Graph of .
- Let . Then the domain of is all such that . The graph is:
- Let . Then the domain of is all such that . The graph is below.
- Let . Then the domain is empty and so there is nothing to graph. (The domain is empty since is only defined for and is only defined for . There are no that satisfy both of these conditions.)