Example  ELF.DIDA.0 Dynamic Visualization of Increasing and Decreasing for Exponential and Logarithmic Functions: Graphs, and Mapping Diagrams

• 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