# Interactive Real Analysis - part of MathCS.org

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## Family Plotter

Lets you plot a one-parameter family of functions in one coordinate system and zoom in using the mouse.

• Click on Options to bring up a dialog window for options
• Modify parameters as you like and click on Apply

The applet helps students to visualize how the shape of a function can depend on a parameter. Enter, for example, the family (x-n)^2, where n goes from -3 to -2 and let students describe what they see.

You can also use the applet to draw a sum, or several partial sums. If you enter, for example, as function xn, check the box "do summation", and let n go from 8 to 8, say, you get the plot of:

S10 = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8

which will of course look similar to 1/1-x - 1 = x/1-x. If n goes from, say, 1 to 8 you will get the plot of S1, S2, ..., up to S8 in one window.

Every partial sum starts at 1. If you need it to start elsewhere, adjust the parameter accordingly.