Graphs and Properties of Exponential and Logarithmic Inverse Functions

This applet demonstrates the inverse relationship between exponential and logarithmic functions. By graphing both functions simultaneously, it visually illustrates their key geometric property: symmetry about the line y=x. Students can explore how swapping the x and y coordinates maps one function's graph onto the other, reinforcing the fundamental concept that inverse functions have interchanged domains and ranges. The interactive nature of the applet allows learners to adjust parameters and observe real-time changes in both graphs, deepening their understanding of functional relationships, symmetric transformations, and the algebraic connection between exponentiation and logarithms. This makes it a valuable visual aid for high school mathematics courses covering function theory and inverse functions.