EXPONENTIAL FUNCTIONS Objectives Evaluate Exponential Functions Graph Exponential

EXPONENTIAL FUNCTIONS Objectives: Evaluate Exponential Functions Graph Exponential Functions Define the Number e

Exponential function � The exponential function with base is defined by where is a positive constant other than 1 and is any real number. � Domain: � THM: For an exponential function if x is any real number then ,

General Characteristics of Exponential Functions of the Form � � � � 1. The domain of consists of all real numbers. The range of consists of all positive real numbers 2. The graphs of all exponential functions of the form pass through the point because. The yintercept is 1. 3. If , has a graph that goes up to the right and is an increasing function. The greater the value of , the steeper the increase 4. If , has a graph that goes down to the right and is a decreasing function. The smaller the value of , the steeper the decrease. 5. is a one-to-one function. 6. The graph of approaches, but does not touch, the x-axis. The x-axis is a horizontal asymptote. There are no xintercepts. 7. The graphs of all exponential functions of the form pass through the points are smooth and continuous.

EX: Graph each function. Determine the domain, range, and horizontal asymptote of each function. � 1. � 2.

EX: Graph each function using transformations. Determine the domain, range, and horizontal asymptote of each function. � 3. � 4.

EX: Graph each function using transformations. Determine the domain, range, and horizontal asymptote of each function. � 5. � 6.

EX: Graph each function using transformations. Determine the domain, range, and horizontal asymptote of each function. � 7. � 8.