Evaluating A Step Function

Section 1.6
Example 2

Please explain Example 2.

See attachment.

I definitely don't understand when x = 2/3.

 

for x=-1, the greatest integer x <=-1 is -1 => imagine a number line x <=-1


as you can see x <=-1 are all integers from -1 to -infinity (all negative integers) and the greatest negative integer is -1
you substitute it in equation
f(-1)=[[-1]]+1=-1+1=0

same reasoning for x =2
x <= 2 are all integers from 2 to -infinity, and the greatest integer x <= 2 is 2


substitute it in equation
f(2)=[[2]]+1=2+1=3

for x=3/2 which is not an integer but lies between integers 1 and 2, then the greatest integer x <= 3/2 is 1


f(3/2)=[[3/2]]+1=1+1=2

 

I will need practice with this stuff.