How to Graph Natural Log and Exponential Functions with Base e

The Organic Chemistry Tutor

This educational mathematics video provides a clear, step-by-step tutorial on how to graph exponential functions with base 'e' and natural logarithmic functions. The instructor demonstrates that the principles used for graphing standard exponential and logarithmic equations apply directly to those involving Euler's number (e), simplifying a concept that often intimidates students. Through two distinct examples, the video breaks down the process of creating tables of values, identifying asymptotes, and sketching the curves on a coordinate plane. The video covers two main examples: graphing an exponential function with horizontal and vertical shifts, and graphing a natural log function with similar transformations. For each example, the instructor teaches a specific method for choosing 'smart' x-values to simplify calculations—setting exponents or log arguments to 0 and 1. The tutorial effectively connects algebraic manipulation with visual graphing, showing how to calculate coordinates using the approximation of e (2.7) and how to determine the domain and range from the final graph. This resource is highly valuable for Algebra II and Pre-Calculus classrooms as it bridges the gap between abstract function transformations and concrete graphing skills. Teachers can use this video to reinforce lessons on inverse functions, domain and range, or as a specific guide for handling the constant 'e' in graphing contexts. The step-by-step approach makes it excellent for differentiated instruction, allowing students to pause and process calculation steps at their own pace.