Domain of f(x):
The domain of consists of all real numbers.

• Range of f(x):
• The range of is the collection of all positive real numbers.

Properties of exponentials: 

1)
2)

• 3)
• 4)   
•  

Increasing exponential function:
If then is an increasing function.

Decreasing function:
If then  is a decreasing function.

Exponential functions are used in mathematics application problems. The operations of exponential functions are defined and used in the examples from this tutorial. Understanding how to plot the graph of an exponential function is important to the discussion of its properties.

Euler’s number known as “e” is a famous one that is commonly used in advanced mathematics course and physical science disciplines. Sample problems of the use of the basic exponential function are shown through the examples.

Specific Tutorial Features:

• Step by step examples are shown to describe the properties and operations of exponentials.
• Solving exponential functions are presented with the use of problem solving techniques.

Series Features:

• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
• Definition slides introduce terms as they are needed.
• Visual representation of concepts
• Animated examples—worked out step by step
• A concise summary is given at the conclusion of the tutorial.

Definition of exponential functions
Properties of exponential functions
          Graph of exponential functions
Euler’s number
Sample Problems of exponential functions