Notice how the arrows on the mapping diagrams are paired with the points on the graph of the functions.
You can move the point for $x$ on the mapping diagram to see how the function value for the function $f(x) =2\cdot \exp_3(x-1) $ changes both on the diagram and on the graph.

Uncheck the upper box to hide the graph and arrows on the diagram for the function $f(x) =2\cdot \exp_3(x-1)  = 2 \cdot 3^{x-1} $.
Check the middle box to show the graph and arrows on the diagram for the function $g(x) = 2 \cdot \log_3(x-1) $.