Abstract: Technology is described herein for initially plotting the mathematical function within an interactive graph, without requiring the user to specify an initial display region of the plot. Techniques are described for automatically determining an appropriate initial range and an initial domain which define the initial display region. The initial range and initial domain are based on the identification of points of the mathematical function that may be interesting to the user. This allows a wide variety of mathematical functions to be plotted and appropriately displayed to users who may lack the mathematical knowledge necessary to select an appropriate display region.

Abstract: Technology is described herein for quickly, efficiently and accurately rendering a plot of the mathematical function within an interactive graph on a web page, such as a search results web page. The technology includes determining a sampling resolution indicating the points of the mathematical function to be plotted within a display region of the plot. The sampling resolution includes a higher number of sample points in sections of the mathematical function with function values that change considerably, and includes a lower number of sample points in sections with function values that change slightly. The interactive graph provides the user with a rich interactive experience that facilitates and encourages the user's understanding of mathematical concepts and underlying principles.