The composition of the core quadratic function $trig(x)=\cos$ followed by the core linear function $f_{-2}(x) = x-2$, so $f(x) = \cos(x) - 2$.

Draw a mapping diagram showing this composition or use the diagram created with GeoGebra to explore the diagram further.

Compare the mapping diagram with the graphs of $\cos(x)$ and $f(x)$

For any $a \gt 0$ the even symmetry with respect to $x=0$ of $f_C$ gives $f_C(+a) = f_C(-a)$