Notice how the arrows on the mapping diagram are paired with the
point on the graph of the function $o(x)$.
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.
Sliders: The slider labeled combop controls whether an arithmetic operation or composition is applied to $f $ and $g$.
For selection of arithmetic operation: 1.
For composition: 2 or 3.
The slider labeled binop appears when combop = 1. It controls which arithmetic operation is applied to $f $ and $g$ as $f$ binop $g$.
Notice the apparent discontinuity of the function that uses division $o(x) = f(x)/g(x)$ on the mapping diagram is
evidenced by the missing arrow as the value of $g(x)$
passes through $0$ when $x=0, \pm \pi,$ and $\pm 2\pi$.
Check the box labeled Show/Hide Table Data to display a selection of data on the graph with points on the graph and with arrows on the diagram to match the data in a table.
The functions $f$ and $g$ can be changed by making entries in the appropriately labeled input boxes.
Martin Flashman, March. 14, 2017. Created with GeoGebra