GRAPHICAL INTERPRETATION OF SENTENCES LIKE $\,f(x) = g(x)\,$ and $\,f(x) \gt g(x)$
  • Click anywhere in the GeoGebra window (below) to make it active.
  • Two functions are graphed:
    $\,f\,$ is a cubic polynomial, in the solid black linestyle
    $\,g\,$ is a parabola, in the dotted black linestyle
  • Click the point $\,P(x,0)\,$ (on the $\,x$-axis) to make it active.
    As you move it along the $\,x$-axis, you can see whether the sentences
    $\,f(x) \gt g(x)\,$,   $\,f(x) = g(x)\,$,   and   $\,f(x) \lt g(x)\,$   are true or false for each value of $\,x\,$.
  • Use the sliders to change the coordinates of two points,  (xint1,yint1)  and  (xint2,yint2) ,
    where the graphs of $\,f\,$ and $\,g\,$ will intersect.
    The graphs will change dynamically to obtain these desired intersection points.
  • You may double-click on the GeoGebra window below to bring up a fully-functioning GeoGebra window;
    this is exactly what you'd get if you download GeoGebra yourself.
  • REFRESH this page at any time to restore it to its initial configuration.
Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and activated. (click here to install Java now)

Dr. Carol J.V. Fisher, Created with GeoGebra