This is best understood as the composition of the linear function $ f_{+C}(x) = x-2$ followed by the core trigonometric function $trig(x) =\cos(x) $, 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 $trig(x)$ and $f(x)$

For any $a \gt 0$ the even symmetry with respect to $x=2$ of $f_c$ gives $f_c(2+a) = f_c(2-a)$