TABLE OF CONTENTS We now shift our attention from sequences to functions. Instead of discrete values a 1, a 2, a 3, , a n, we will explore a continuum of values represented by f( x).
A function is one of the most important concepts in mathematics. It is usually an algebraic expression whose value depends on the value we assign to some variable. For example, x 2 + 1 is a function of x. If we set x = 2, then x 2 + 1 = 5. Then symbol f( x) is a short way to write the function of an independent variable x. (Sometimes just f is sufficient.) We read this as " f of x," and for this example we write f( x) = x 2 + 1. The number f( x) is produced by the number x. Notice that f( x) does not mean " f times x." It is a single, indivisible symbol standing for some function.
In the equation y = f( x), the value of y depends on the value of x. The function f( x) is some expression or rule that processes the values of x that we input and produces as output a value of y. We call x the independent variable...
