Can someone help with my calc homework?

Here's one possibility.....it's known as the greatest  interger function :

https://www.wolframalpha.com/input/?i=greatest+integer+function

It's denoted   as    shown here   : 

http://www.mathwords.com/c/ceiling_function.htm

Note

lim  f(x)     =    1        

x → 2^- 

But

lim  f(x)     =    2        

x → 2⁺

For more of an explanation to your first and second question. The first question means when you have a function and (x) approaches (a) from the left side (that's why there is a negative sign). You are trying to determine what the function is behaving as (x) approaches (a) from the left. The same applies for positive, however, as you might imagine you'll try to determine from the right as (x) approaches (a). This is important in respects to school knowledge as a function may not behave the same on the negative side of a as (x) approaches (a) and vice versa for the positive side. That's why there is a proof to graph a function where the behavior is different as (x) approaches (a) from the left (negative) and right side (postive) so you'll be able to understand this concept (if you haven't by the time of this post).