Example OW.0  An Implicit (Piecewise) Case Defined Function.

This example presents a (piecewise) case defined function \$f\$, implicitly defined with respect to the equation \$G(x,y) = x^2+y^2−4=0\$ with a table of data, a graph and a mapping diagram.

Notice how the arrows on the mapping diagram are paired with the points on the graph of the equation \$G(x,y) = x^2+y^2−4=0\$.
You can move the point for \$x\$ on the mapping diagram to see how the function value changes both on the diagram and on the graph.
Notice the discontinuity of the function on the mapping diagram is evidenced by the sudden jump in the arrow as the value of \$x\$ passes through \$0\$.
Check the upper box to show the graph with points on the graph and arrows on the diagram to match the data in the table.
Once visible  after checking the upper box you can change the slider for \$n\$, a number that controls the number of points and arrows shown. \$n\$ ranges from \$1\$ to \$10\$.
Check the lower box to show the confirmation that the paired data do satisfy the equation: \$G(x,y) = x^2+y^2−4=0\$.
This confirmation also appears in the third (hidden) column of the spreadsheet.

Martin Flashman, Nov. 9, 2013. Created with GeoGebra