Graph given equation.

Question

Graph the given equation: y=2[[x]]

Answer 1

[[x]] = greatest integer less than or equal to x

 

2[[x]] = 0, if 0≤x<1

 

         = 2, if 1≤x<2

 

         = 4, if 2≤x<3

 

         = 6, if 3≤x<4, etc

 

To graph the function, for x≥0, proceed as follows:

 

Between x=0 and x=1, draw a horizontal line segment with left endpoint (0,0) and with deleted right endpoint (1,0). 

 

Between x=1 and x=2, draw a horizontal line segment with left endpoint (1,2) and with deleted right endpoint (2,2).  

 

Between x=2 and x=3, draw a horizontal line segment with left endpoint (2,4) and with deleted right endpoint (3,4).

 

etc

 

For x < 0, proceed as follows:

 

Between x=-1 and x=0, draw a horizontal line segment with left endpoint (-1,-2) and with deleted right endpoint (0,-2).

 

Between x=-2 and x=-1, draw a horizontal line segment with left endpoint (-2,-4) and with deleted right endpoint (-1,-4).

 

etc 

 

The complete graph looks like a series of steps without the vertical part of each step.