Example  DOM.L.3.  Suppose $h(x)=log_2(2x+5)$. Visualize the domain of $h$ on a mapping diagram.
Solution: The domain of the function $h$ is visualized both on the graph and the mapping diagram by a green open ended ray on the "$X$-axis". 

Comment: Here we consider $g(x) = 2x +5$ and the domain is $\{x : 2x+5 >0\} = (-2.5, \infty)$.
The mapping diagram visualizes $h$ as a composition which shows how the domain of $h$ is determined by the domain of $\log_b$.

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The GeoGebra mapping diagram can be used to visualize the domain for other compositions where $h(x)=f(g(x))=\log_b(g(x))$ .
Try $g(x)=|x|, g(x)=x^2−4$ and $g(x)=4−x^2$.

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