Notice how 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 $f(x) =A\cdot \exp_b(x-h) + k$ changes both on the diagram and on the graph.
Use the sliders to adjust the values for the base, A,h, and k.  $y_{zoom}$ will adjust the scaling on the target axis.

Uncheck the upper box to hide the graph and arrows on the diagram for the function $f(x) =A\cdot \exp_b(x-h)  = A\cdot b^{x-h} +k $.
Check the middle box to show the graph and arrows on the diagram for the function $g(x) = A \cdot \log_b(x-h) +k $.