Example TRIG.SYM.2  :$ A=B=1; trig(x) = \cos(x); C =0; D = -2;$ f(x)=cos(x)-2$

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 $f(x)$

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