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 $.