Example OAF.COMP.2 with SAGE

Example OAF.COMP.2 :$ f(x) = x - 2; g(x) = \frac 1 x$
The composition of the core negative power function $g(x) = \frac 1 x$ followed by the core linear function $f(x) = x-2$, so $R(x) = f(g(x)) = \frac 1 x - 2 = \frac {1-2x} x$.
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 $f(x)$

Given a point / number, $x$, on the source line, there is a blue arrow meeting the target line at the point / number, $\frac 1 x - 2$
This point corresponds to the rational function's value for $x$.
The values for the core mapping diagram for $x-2$ in red are applied to the values $g(x) = \frac 1 x$ (green) .

As $x$ increases, $q(x)$ decreases to value $q(0)=-2$ and then increases.