15.5 Outline

A.  Definitions
      1. first/second components
      2. function
B. Representations
      1. ordered pairs
      2. mapping
      3. machine
C. Functional notation
      1. domain
      2. range
      3. difference quotient
D.  Vertical line test

15.5 Essential Ideas

A function is a set of ordered pairs in which the first component is associated with exactly one second component.  Use the vertical line test to see if a given graph is a function. 

Here are some important functions:
      constant function:      f (x) = k
      linear function:           f (x) = mx + b           (m is not zero)
      quadratic function:     f (x) = ax² + bx + c  (a is not zero)
      exponential function: f (x) = b^x                   (b > 0, b is not one)
      logarithmic function: f (x) = log_bx               (b > 0, b is not zero, x > 0)
      probability function: A function P which satisfies the following properties:
                                        0 <= P(E) <= 1
                                        P(S) = 1                              (S is the sample space)
                                        P(E or F) = P(E) + P(F)    (E and F are mutually exclusive)