Draw the graphs of some functions

Draw the graphs of the functions defined below on the interval $[-2,2]$ , and if it is a step function find a partition $P$ such that the function is constant on the open subintervals of $P$ .

$f(x) = x + [x]$ .
$f(x) = x - [x]$ .
$f(x) = [-x]$ .
$f(x) = 2[x]$ .
$f(x) = \left[x+\frac{1}{2} \right]$ .
$f(x) = [x] + \left[ x+ \frac{1}{2} \right]$ .

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, $P = \{ -2,-1,0,1,2 \}$ . The graph is below.
This is a step function and it is constant on the open subintervals of the partition, $P = \{ -2,-1,0,1,2 \}$ . The graph is below.
This is a step function and it is constant on the open subintervals of the partition, $P = \left\{ -2,-\frac{3}{2},-\frac{1}{2},\frac{1}{2},\frac{3}{2},2 \right\}$ . The graph is below.
This is a step function and it is constant on the open subintervals of the partition, $P = \left\{ -2,-\frac{3}{2},-1,-\frac{1}{2},0,\frac{1}{2},1,\frac{3}{2},2 \right\}$ . The graph is below.

8 comments

April 16, 2019 at 7:35 am

Hanz Marin says:

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

June 7, 2016 at 1:11 pm

Sebastian says:

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.

- May 28, 2017 at 8:07 pm
  
  123456grimmjaw says:
  
  Nevermind, i got it XD
  
May 21, 2016 at 8:37 pm

Yassin says:

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

- May 21, 2016 at 8:52 pm
  
  RoRi says:
  
  Yeah, they should. I’ll fix it. Thanks for letting me know!
  
  - May 22, 2016 at 7:48 am
    
    Yassin says:
    
    Thank you for this amazing web site, listen i am solving the book Introduction to Linear Algebra written by Serge Lang, if you want i can salve my solutions and send to you maybe can be usefull :) I am sorry if i wrote wrong some phrase, actually english is not my native language haha.
March 25, 2016 at 6:03 pm

Leonardo says:

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

- March 31, 2016 at 8:23 am
  
  RoRi says:
  
  Thanks! Fixed.

Stumbling Robot

Draw the graphs of some functions

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