Functions
The whole idea of math is to translate information from the real world into numbers and symbols we can manipulate to predict things. Each branch of math translates information a little differently.

Arithmetic uses numbers. We convert a pile of apples into a certain number of apples then manipulate this number using the rules of addition, subtraction, multiplication and division.

Algebra primarily uses polynomials. We express the things we don’t know in terms of the things we do and wind up with bundles that contain both numbers and unknowns. We call these bundles polynomials, and algebra is the process of manipulating them.

Calculus uses more general functions. A function is a mathematical process we perform on a number. It can be a simple process, like “double the number,” or it can be more complex, like “square a number, then double the result, then subtract the speed of light from it.” Some processes lead to more than one correct answer. Years ago they categorized functions according to how many correct answers they could generate. There were “one valued functions,” “two valued functions,” etc. That is, if you applied the procedure to a certain number, how many correct answers would it yield? Today we only consider “one valued” functions to be true functions. Other math procedures are not functions and don’t get to play with us right now.

Cats think of functions as precise little dances. If they begin the dance at one location and perform each step correctly they arrive at some particular spot. If you know where they start, you’ll know where they end. It also works in reverse: if you know where they end up, you know where they started.
One cat, let’s call him “Garfield” (after the president), always does the dance called the watusi. The dance is very precise: he takes four steps forward, two steps to the side, eats a snack, then manages one more step forward, then settles down for a long and well-deserved nap. The dance is made up of all these steps. Simply shortening it to “watusi” helps a bit. But in math, we can’t possibly name each and every combination of procedures. So we give them the general name of function and then describe them in more detail for each problem.

If you see watusi (x) in a problem, you know what dance Garfield does and that he starts at x. If you know where to start, you’ll know where he ends up.

watusi(starting spot) = ending spot

As you begin studying functions they will usually use the letter ƒ to represent an entire function. As you encounter situations involving more than one function, they will most often use g or h to symbolize different functions. If something is a function of time, it’s not uncommon to use t to represent time.

Different cats do different dances so we need to label them appropriately. We don’t want Garfield break-dancing when he’s supposed to be waltzing. When we write down a function we’ll always have two elements: the abbreviation for the procedure, and then next to it (in parentheses) the name of the starting spot.When we see

ƒ(x)

we know that ƒ is the abbreviation for the procedure and x is the character that will have that procedure done to it.

Here’s a great opportunity for confusion. You have always thought that when you saw something in parenthesis you were going to be multiplying. Those days are over. If you see an ƒ before parentheses, they are NOT telling you to multiply ƒ times the contents of the parentheses. They’re telling you that you will perform the ƒ function upon whatever is inside the parentheses. In the same problem we might see

g(t)

and we know that g represents a procedure we’re going to do to t as soon as we know what number it represents.

Here’s another fun way to confuse you: the first time you see ƒ(x) in a problem, they are probably defining the function for you. They will say ƒ(x) equals something, and that’s how they let you know what to substitute.

ƒ(x) = 2x +34 - x2

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Obviously I'm practicing my writing on this web area that you should not be able to see because I need to make thisalgebra unplugged, math book. kenn amdahl jim loatsclearwater publishing company publishes Kenn Amdahl books in Colorado. Clearwater Publishing Company publishes educational fun books. Books include There Are No Electrons Electronics &lt;span class=&quot;style8&quot;&gt;for Earthlings, Algebra Unplugged, Calculus for Cats, Joy Writing: Discover and Develop your Creative Voice, The Land of Debris and the Home of Alfredo. Clearwater also publishes The Barefoot Fisherman: a fishing book for kids by Paul Amdahl. and Economics for the Impatient by C.A. Turner. Our books are about science, math, creative writingg algebra, calculus s, economics, fishing, kids, parenting, education. Curriculums like them, and so do home schoolers. Joy of Writing and The Joy of Writing are not our books, but Joy Writing is. Kenn Amdahl is president. He's a songwriter and author in Broomfield Colorado. Electronics, teaching electricity, teaching math, especially alebra and calculus and creative writing. SAT, LSAT, and other test takers may like these books. They are like books for dummies, algebra for dummies, calculus for dummies, creative writing for dummies, fishing for dummies, parenting for dummies . Or Algebra for Idiots, Calculus for Idiots, Creative Writing for Dummies. Memoir writing or memoir writers may find Joy Writing useful, although it is not The Joy of Writing or the Joy of Sex or the Joy of Algebra for that matter. They are not chicken soup for the writers soul, or algebra for the writers soul, or calculus for the writers soul. They are not strictly speaking Christian or religious or spiritual, but those folks are welcome. Jesus would not disapprove of these books. Jesus might like them. The Rapture of Writing might be a good title. Self-publishers read our books, Dan Poynter is recommended. 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Release a CD Write a book and self publish it. Groups we like include Book Organizations of Colorado, Colorado Independent Publishers Association CIPA Colorado Authors League Rocky Mountain Fiction Writers Pikes Peak Writers Aspen Writers Mountains and Plains Booksellers Independent Booksellers SPAN Small Press Association of North America Publishers Association of the WEst Colorado Library Association Last Note Singers Cottonwood the music group. Edward Ormondroyd and George Garrett gave blurbs to our books </span></div>
square bigger and have not learned how yet except to type in words, poetry, prose, language, steinbeck type stuff, No Child Left Behind, that's my motto. Naked books, with no girls gone wild, no bikini models no first amendment problems. no amateur index ladies or lightspeed girls or coeds or women. Just books about electricity, like Tesla or Edison might write, books about Algebra like Aristotle might write. Calculus books like Garfield the cat might write. Cat stuff, feline stuff, study guide type raw material. Books for girls who like to read and boys who know how to. Teach yourself math, science, fishing, in clear water or clearwater economics creative writing and poetry. Sing a song. Release a CD Write a book and self publish it. Groups we like include Book Organizations of Colorado, Colorado Independent Publishers Association CIPA Colorado Authors League Rocky Mountain Fiction Wri</span><span class="style11">ters Pikes Peak Writers Aspen Writers Mountains and Plains Booksellers Independent Booksellers SPAN Small Press Association of North America Publishers Association of the WEst Colorado Library Association Last Note Singers Cottonwood the music group. Jill Wagner is the actress in the Mercury Mariner TV commercial. Jill Wagner will become a big star and people will google her. That's Jill Wagner, mercuryvehicles.com, TV actress. She's in Vancouver filming a movie.Edward Ormondroyd and George Garrett gave blurbs to our books </span></div>