Time to start doing math again

I awoke last night from uneasy dreams not to find myself transformed into a monstrous vermon, but to find it wasn't real.  When I was in graduate school for psychology, I developed a love for statistics (weird, huh?).  I took all the stats classes in the psychology department.  Then I took all the stats classes in the school of education (or nearly all).  Finally, I decided to start taking classes in the math department and to get a master's degree in mathematical statistics.  Alas, I hadn't taken calculus since high school (or any math other than stats, for that matter).  The department required two semesters of single variable calculus, a course on multivariable calculus, a course on differential equations, a course on linear algebra, a course in computer programming (I took two, because they were so fun), and a course in calculus-based statistics.  So, I worked my way through the pre-requisites.  I excelled in stats and computers, but always had trouble with the math.  However, sometimes I could do well in the math classes when I could incorporate the computer.  In differential equations, I modeled the transverse vibrations of a beam using a piece of software called MAPLE, common in math circles but not so common anywhere else.  I've been out of grad school for over six years now.  In my dream last night, I was talking to the undergraduate advisor from the math department; I always liked him a lot.  He was a white haired man as long as I knew him; now, he let his hair grow long and he died it dark, but the white was coming in such that he looked salt-and-pepper.  Apparently, I was in my last semester of graduate school and none of my funding options came through, so I was not teaching anything and not taking any classes.  I was also informed I needed one more math class and two more stats classes, so I had to take classes again. The math class was a pre-requisite to the stats class, but the first stats and the last math could be taken concurrently.  So, I scoured the catalog, and my DiffEq teacher was teaching a class on computer programming for math people for which I registered.  I also took the first stats class (which was a biostats class that covered a lot of what I already knew).  I was a bit nervous about the computer class.  In addition to classes I was taking, the math department decided they'd have me teach a class in "statistical modeling and algebra," though call it "university algebra."  In real life, when I was doing my stats degree, they had me teach "university algebra," and I expected never to do it again -- but I was.  Anyway, I woke up a bit disconcerted and went to check that I indeed have my degree; I did.  Then, I looked to see if such a class was offered; it was not.  But, I'd like to be better and the math and not fear said situation.  So, I pulled my calculus book off my self and said to myself, "Self, it's time to start doing math again."  I pulled down my calculus book, opened to the first problem (#1 on page 35), and this is where I am:

Problem #1:

Classify each function as a power function, root function, polynomial function (state its degree), algebraic function, trigonometric function, exponential function, or logarithmic function.

1 (a) f(x) = ⁵√ X
   (b) g(x) = √(1-x⁵)
   (c)  h(x) = x⁹ + x⁴
   (d)  r(x)  = (x²+1) / (x²+x)
   (e) s(x) = tan 2x
   (f) t(x) = log₁₀x

ANSWERS:

(a)  Root
(b)  Algebraic
(c)  Polynomial of degree 9
(d)  At first glance, I thought Algebraic, but realized that the denominator could be factored as x(x²+1).  Written, that way, it's easy to see how the numerator and the second term cancel, leaving me with r(x) = 1/x.  That's a Rational function (and my high school pre-calculus teacher, Chuck Hanes [who worked for NASA before they moved him so much he had to stop working for NASA and decided to teach high school would call a "ya hee ya ha").  I guess I'm remembering some stuff after all..
(e)  Trigonometric
(f)  Logarithmic

That was easy -- but it's chapter 1.  Then, I realized I started in section 2 of chapter 1.  Tomorrow, I'll go back and work on section 1.