Remember that the function f(x)=[ [ x ] ] is a step function.
We want to graph the given function.
f(x)= [ [ x ] ]
To do so, we need to recall that the symbol [ [ x ] ] means the greatest integer less than or equal to x. For example, [ [ 2.1 ] ] =2, [ [ 2.9 ] ] =2, and [ [ - 1.5 ] ] =- 2. Remembering this rule, let's make a table of values for the given function.
x
[ [ x ] ]
f(x)=[ [ x ] ]
- 2
[ [ - 2 ] ]
- 2
- 1.5
[ [ - 1.5 ] ]
- 2
- 1
[ [ - 1 ] ]
- 1
0
[ [ 0 ] ]
0
1
[ [ 1] ]
1
1.5
[ [ 1.5] ]
1
2
[ [ 2 ] ]
2
3
[ [ 3 ] ]
3
3.5
[ [ 3.5 ] ]
3
We can plot these points on a coordinate plane. Since the function f(x)=[ [ x ] ] is a step function, we need to remember that the right endpoint of each segment will be an "empty point."
