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 $f(x)$
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.