Notice how the arrows on the mapping diagrams are paired with
the points on the graph of the functions.
You can move the point for $x$ on the mapping diagram to see how the function value for the function $ f(x) = 2\cos(x-1)+1$ changes both on the diagram and on the graph.
Notice how the graph and mapping diagram visualize the fact that for the cosine function, $2\cos(x-1)+1$ has the same basic shape as $\cos(x)$ though its axis of symmetry has changed to $x=1$.
Check the box to show points on the graph and arrows on the diagram
for the function $ f(x) =2\cos(x-1)+1$.