4.1 Exponential Functions and Their Graphs Transformation, k Horizontal: shift left: ; shift right: Vertical: Shift down: ; Shift Up: Inverse of Exponential is Logs: Continuous Compounding:

A graph of an exponential function is given by the equation: Inc: Increasing exponential function when either x is positive and b is greater than 1 Example: (a) (b) Dec: Decreasing exponential function when either x is negative or b is less than 1 but greater than 0 Example: (a) (b) Domain: Range: Some Properties with Radicals - by Examples (a) (b) Periodic Compounding: P = initial amount, r = annual rate (decimal) n = number of compound period per year

4.3 Logarithmic Functions and Their Graphs Inverse of log is Exponential

For , then is same as Common Log: Natural Log : Domain: Range: Properties (a) (b) (c) Examples: (a) (b) (c)