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