4.4, due February 7

OK. So apparently everything my algebra teacher told me was a lie.  Well, maybe it wasn't a lie but it wasn't completely accurate.  I always thought that "x" only had one meaning in a function.  Actually it has two and it depends on how you are thinking about it as to which meaning "x" takes on.  If you are thinking of "x" in the context of R[x], then "x" is an element.  If you are thinking of "x" in a polynomial function, "x" takes on the standard algebraic role of the variable to define a function f: R -> R.  I felt like most of this section was clarifying all the falsities our algebra teachers taught us in high school.  The one thing that I have found that frequently gives me grief is distinguishing between f(x) and F[x].  When you read them to yourself or out loud to your imaginary friend, they sound the exact same, "f of x". I often find myself confused about which f, and now, which x I'm talking about.  Is that big F or little f? Is x the variable or is it an element? PotAtoe, potatoe? I have a feeling we can't call this one off....