Draw the graphs of the functions defined below on the interval , and if it is a step function find a partition such that the function is constant on the open subintervals of .

- .
- .
- .
- .
- .
- .

- This is not a step function. The graph is below.
- This is not a step function. The graph is below.
- This is a step function and it is constant on the open subintervals of the partition, . The graph is below.
- This is a step function and it is constant on the open subintervals of the partition, . The graph is below.
- This is a step function and it is constant on the open subintervals of the partition, . The graph is below.

Shouldn’t partitions points be the ones inside the interval? I mean, not considering the extreme points?

Dude i might be wrong but shouldn’t graph c be one to the right, cause de interval from -2 to -1 should be on 2 on the y axis.

Nevermind, i got it XD

in th graph c should not be open on left side of each point of the partition and closed on the right side?

Yeah, they should. I’ll fix it. Thanks for letting me know!

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Graph in part e), the last point should be filled as when x=2 f(x)=2

Thanks! Fixed.