    - page 10, "Finally ... Functions"

Functions

Functions are dependable -- sophisticated operations or sequences of operations given a special name because they are used so often and because each specific argument yields the same answer, a unique answer, each time the function operates. The arguments are in the function's domain.

The arithmetic operations in the left column below are functions in their role in precalculus. Most of these functions have already been examined. Others are found on the Functions and Operations Page. Still others are listed on the right. Still others exist but aren't even listed.

So. As promised, the most sophisticated has top priority. Now, the Order of Operations is:

THE ORDER OF OPERATIONS (Topmost First)
• Functions
• Parentheses or other Marks of Inclusion (Innermost First)
• Roots or Exponents
• Multiplication or Division (Leftmost First)
• Addition or Subtraction (Leftmost First)

Restated it's: Functions, Parentheses first, next Roots or Exponents, then Multiply or Divide (left to righ) then Add or Subtract (left to right): Finally Please, Readily Excuse, My Dear Aunt Sally.

Functions:
NAMED OPERATIONS Performed on ARGUMENTS from a DOMAIN

Three ideas -- NAMED, OPERATIONS, ARGUMENTS -- were introduced in the above working definition of functions.

" Functions are operations or sequences of operations given a name because they are often used and because each argument yields a unique answer.

An other idea -- DOMAIN -- stratefies the sophistication of the user. Parents don't tell children everything about life. Teachers don't tell students everything about the domains of functions.

Reconsider the functions listed above and the specifics listed here about the functions. Also:

• The function symbol f(x) -- read as "f of x" -- is listed then for function whose symbols are difficult to write with a typewritter, a calculator or math computer symbol is listed.
• If the function requires more than one argument, it will have additional variable placeholders to indicate how many or which arguments are needed.
• Comments on the domain may be listed.

 absolute value cosine f(x)= cos(x) cube f(x)= x³ = (x)(x)(x) cube root exponential identity f(x)= x log natural log opposite f(x)= -x reciprocal sine f(x)= sin(x) square root Before algebra II, the domain is nonnegative numbers. square f(x)= x² = (x)(x) tangent f(x)= tan(x)     The reader is asked to visit briefly the Functions and Operations Page before completing the questions on the next page.              © 2005, Agnes Azzolino www.mathnstuff.com/math/spoken/here/2class/80/c80j.htm