Martin Flashman, May 31, 2016. Created with GeoGebra

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 $.