Question 1132478
Consider the graph of each function and decide if it is continuous
y=[x]

<pre>I think you mean the "floor" function where y is the SMALLEST
integer that does not exceed x.  It's a "stair-step" function.  
Examples:

[π] = [3] = [&#8730;<span style="text-decoration: overline">10</span>] = [3.001] = [3.999] = 3

[-π] = [-4] = [-&#8730;<span style="text-decoration: overline">10</span>] = [-3.999] = [-3.001] = -4

but [-3] = -3 and [-4] = -4

{{{drawing(400,400,-10,10,-10,10,

graph(400,400,-10,10,-10,10),

line(-10,-10,-9,-10),circle(-10,-10,0.15),circle(-10,-10,0.1),circle(-9,-10,0.15),
line(-9,-9,-8,-9),circle(-9,-9,0.15),circle(-9,-9,0.1),circle(-8,-9,0.15),
line(-8,-8,-7,-8),circle(-8,-8,0.15),circle(-8,-8,0.1),circle(-7,-8,0.15),
line(-7,-7,-6,-7),circle(-7,-7,0.15),circle(-7,-7,0.1),circle(-6,-7,0.15),
line(-6,-6,-5,-6),circle(-6,-6,0.15),circle(-6,-6,0.1),circle(-5,-6,0.15),
line(-5,-5,-4,-5),circle(-5,-5,0.15),circle(-5,-5,0.1),circle(-4,-5,0.15),
line(-4,-4,-3,-4),circle(-4,-4,0.15),circle(-4,-4,0.1),circle(-3,-4,0.15),
line(-3,-3,-2,-3),circle(-3,-3,0.15),circle(-3,-3,0.1),circle(-2,-3,0.15),
line(-2,-2,-1,-2),circle(-2,-2,0.15),circle(-2,-2,0.1),circle(-1,-2,0.15),
line(-1,-1,0,-1),circle(-1,-1,0.15),circle(-1,-1,0.1),circle(0,-1,0.15),
line(0,0,1,0),circle(0,0,0.15),circle(0,0,0.1),circle(1,0,0.15),
line(1,1,2,1),circle(1,1,0.15),circle(1,1,0.1),circle(2,1,0.15),
line(2,2,3,2),circle(2,2,0.15),circle(2,2,0.1),circle(3,2,0.15),
line(3,3,4,3),circle(3,3,0.15),circle(3,3,0.1),circle(4,3,0.15),
line(4,4,5,4),circle(4,4,0.15),circle(4,4,0.1),circle(5,4,0.15),
line(5,5,6,5),circle(5,5,0.15),circle(5,5,0.1),circle(6,5,0.15),
line(6,6,7,6),circle(6,6,0.15),circle(6,6,0.1),circle(7,6,0.15),
line(7,7,8,7),circle(7,7,0.15),circle(7,7,0.1),circle(8,7,0.15),
line(8,8,9,8),circle(8,8,0.15),circle(8,8,0.1),circle(9,8,0.15),
line(9,9,10,9),circle(9,9,0.15),circle(9,9,0.1),circle(10,9,0.15) )}}}

As you see it is not at all continuous.

Edwin</pre>