- Move the $b$ slider to change the value of $b$.
- Uncheck a box to remove that function's graph and mapping diagram.
- Notice the connection between $b$ and the general features of the functions.
- Select the point $x$ in the mapping diagram to move the point by mouse or use the scroll up or down key to move the $x$ by increments of 0.1.
- Move the $y_{zoom}$ slider to change the scale on the Y axis of the mapping diagram.
- Notice how the graph and mapping diagram visualize the facts:

For exponential and logarithmic functions, - if $b>1$ then
$exp_b$ and $\log_b$ are increasing functions; when $x<0$ and $x$
is large in magnitude, then $exp_b(x) \approx 0$, while when $x>0
$ and $x \approx 0$ then $\log_b(x) <0$ and very large in magnitude.

- if $0<b<1$ then $exp_b$ and $\log_b$ are decreasing functions; when $x>0$ and $x$ is large in magnitude, then $exp_b(x) \approx 0$, while when $x>0 $ and $x \approx 0$ then $\log_b(x) >0$ and very large in magnitude.

Martin Flashman, Jan. 10, 2014. Created with GeoGebra