Visualizing and Evaluating Inverse Functions on a Graph

Miacademy & MiaPrep Learning Channel

This educational video introduces the concept of inverse functions through a graphical approach. It begins by defining an inverse as a function that swaps inputs and outputs, providing practical examples of why this is useful, such as reversing mathematical relationships like temperature conversion. The video then demonstrates how to find an inverse function graphically by swapping the x and y coordinates of specific points on a linear function and plotting the result. A key visual theme explored is the geometric relationship between a function and its inverse, showing that they are reflections of each other across the line y = x. The narrator emphasizes that if a point (a, b) exists on the original graph, the point (b, a) exists on the inverse graph. This visual symmetry provides an intuitive way for students to check their work when graphing inverses. The final segment of the video focuses on evaluating inverse functions using function notation. It clarifies common confusion regarding the negative one exponent notation, explaining that it denotes an inverse rather than a reciprocal. The video provides a practical shortcut for evaluating inverses without graphing them entirely: finding the input on the original graph that corresponds to the specific output requested by the inverse function.