Introduction to Exponential Functions: Graphing and Transformations

The video tutorial explores the function y = e^x, focusing on its gradient function and the special constant e. It explains how e is a natural exponential constant, similar to pi, and discusses the properties of the graph y = e^x, including its intercepts and asymptotic behavior. The tutorial also covers variations of the graph, such as reflections and transformations, and provides detailed examples of how to apply these transformations to sketch different exponential graphs.

What is the significance of the point (0, 1) on the graph of y = e^x?

Explain the concept of exponential decay in relation to the graph of y = e^(-x).

How do transformations affect the graph of y = e^x?

How does the value of 'a' in the function y = a^x affect the graph?