Functions is a large subject, so I'm not quite sure on what to tell you. Everyone else is right that you will get a lot of this in later years. In Algebra 2 and Trig/Pre-Calc, you'll do a -lot- with functions. They're really important once you get to Calculus, so it's not surprising that they hammer it in during those two courses.
Anyway, "In mathematics, a function relates each of its inputs to exactly one output." (WP) The trickiest thing about them is that each function can only have one y-value for every x-value it has. For instance, if I had the following set:
{(3,4) (4,7) (3,6)}
It would not be a function. This is because two x-values (3) are the same, and are matched with two different y-values (4 and 6). If you are given a set, and need to find if it's a function, simply graph it and do the "Vertical Line Test." Take a pencil (Or anything straight) and make it vertical on the graph. If, when you move the pencil around, the pencil intersects your graph more than once, it is not a function (Here's a picture that will better show the Vertical Line Test:
http://en.wikibooks.org/wiki/Image:Vertlinetest.png ).
Basic functions are simple, like the one that you posted. Most are used more as a graph than a simple equation, but graphing it is no more difficult than solving for a bunch of different values.
More advanced functions included squares, cubes, inverses, and a bunch more. I'll try to give a brief explanation:
With any function f(x)=x^2, the function will take the form of a parabola (
http://en.wikipedia.org/wiki/Image:Parabola.svg) . The exact placement is sometimes important, which can be found using the process here
http://tutorial.math.lamar.edu/AllBr.../Parabolas.asp . This website even tells you how to sketch the graph.
http://tutorial.math.lamar.edu/AllBr...cFunctions.asp - This also goes over the basics of sketching other graphs, such as f(x)=|x|,
f(x)=x^3, and f(x)=sqrt(x)
When asked to graph the inverse of the function, all you need to do is switch the x- and y-values of every point. If the points of my original function were:
(3,4) (5,6)
Then the points of the inverse would be:
(4,3) (6,5)
To find it algebraically, you take your original equation (We'll use the one you posted originally, f(x)=x+3) and you swap the y and x variables in the equation. For all practical purposes, f(x) is the same as y. Then, once you do the switch, solve for y. Here's an example:
f(x)=x+3 Replace f(x) with y
y=x+3 Switch the x and why variables
x=y+3 Subtract 3 from each sides
x-3=y Then rearrange the equation so it looks pretty
y=x-3
Done! Of course, some inverses can get pretty complicated. But that's a pretty easy example.
That's all I can remember right now... Nothing that I said in this post will get anywhere near what you'll learn in a class. I haven't done functions and a while, and I've never been a teacher... So don't take this as anymore than a bunch of jumbled memories. If you'd like to learn some more, use these two sites:
http://en.wikibooks.org/wiki/Algebra:Functions http://en.wikipedia.org/wiki/Function_%28mathematics%29 (Which was earlier cited as WP)
http://en.wikibooks.org/wiki/Calculus:Functions
The first one will help you the most, it's the entry look at functions. The second one is just an overview. The third one is a look at functions from a Pre-Calc and Calculus perspective.
It's a good thing you're trying to prepare for college and willing to learn math so beyond your level, but don't spend too much time preparing for you SAT already. You'll have lots of time to stress over it in Sophomore and Junior year.
I hope I was some help... If you have any more math questions, search for them on en.wikibooks.org. If you can't find them there, you can email me any other questions you have (Ateowa@**********), and I'll do my best to help. Good luck=)
EDIT: Forgot a link
