A core exponential function has the form $\exp_b(x) =
b^x$ where $b > 0$, $b \ne 1$.
For example in ELF.0: $f(x) = \exp_2(x) = 2^x$.
A core logarithmic function has the form $\log_b(y)$
where $b > 0$, $b \ne 1$, and $ y \in (0,\infty)$.
For example in ELF.0 : $g(x) = \log_2(y)$.
We explore how mapping diagrams for core
exponential and logarithmic functions help us visualize and
understand further the meaning of the shape of the graphs of these
functions .
Example ELF.CELF.2
: $b=
\frac 1 2 ; f(x) =\exp_{\frac 1 2}(x) = (\frac 1 2)
^x$ and $g(x)= \log_ {\frac 1 2} (x)$.
Example
ELF.DCELF.0 : Dynamic Visualization of Core
Exponential and Logarithmic Functions: Graphs and Mapping Diagrams