Graphs of $g(x)$ and $q(x)$

Mapping Diagram Showing Composition.
Given a point / number, $x$, on the source line, there is a
blue arrow meeting the target line at the point / number,
$\frac 1 2 x^2$. This point corresponds to the quadratic function's value for $x$. The values for the core mapping diagram for $x^2$ in green are magnified by a factor of $\frac 1 2$ shown by the red arrows. 