Horizontal Line Test

This applet can be used to determine whether a function is one-to-one or not, and also to restrict the domain to some interval where the function is one-to-one.

• Enter a function of x in the input box.
• Drag the vertical slider up or down (or press the Play button) to find the intersecting points of the graph and the horizontal line.
• To see the x-coordinates of the intersection points, check the “show coordinates”.

If we want to define an inverse function then we have to find an interval where f(x) is one-to-one.

• Drag the left and/or the right side of the blue segment under the graph to restrict the domain.

Use the second button on the toolbar to drag the viewing window, zoom in or zoom out if necessary.

Irina Boyadzhiev, 18 September 2013, Created with GeoGebra