Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Quadratic Equations And Polynomials
Introduction: The Reflection Property
When a function and its inverse are graphed on the same coordinate plane, a beautiful geometric relationship emerges: the graphs are reflections across the line y=x. This property provides a visual way to understand inverse functions and to check whether two functions are inverses.
The Reflection Property
If a point ablies on the graph of f(x), then the point balies on the graph of f-1(x). This is because the inverse swaps the roles of input and output.
Geometrically, this means the graph of f-1(x)is the mirror image of the graph of f(x)across the line y=x.
How to Graph an Inverse Function
Method 1: Algebraically Find the Inverse, Then Plot
- Find the inverse function algebraically
- Create a table of values for the inverse
- Plot the points and draw the graph