Example QF.COMP.3 :$ f(x) = 2x ; g(x) = x^2$
The composition of the core quadratic function $g(x)= x^2$ followed by the core linear function $f(x) = 2x$, so $q(x) = f(g(x)) = 2x^2 $.
Draw a mapping diagram showing this composition  or have SAGE create this by evaluating.
Compare the mapping diagram with the graphs of $g(x)$ and $f(x)$
Graphs of $g(x)$ and $f(x)$
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, $2 x^2 $
This point corresponds to the quadratic function's value for $x$.
The values for the core mapping diagram for $2x$ in red are  applied to the values $g(x)=x^2$ (green) .

As $x$ increases, $q(x)$ decreases to value $q(0)=0$ and then increases.