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 $ h(x) = \cos(x -2)$ changes both on the diagram and on the graph.
The arrow on the point on the mapping diagram target axis indicates whether the value of the function $h(x)$ is increasing (pointing up) or decreasing (pointing down).

Notice how the graph and mapping diagram visualize the fact that for the cosine function, $\cos(x-C)$  has the same basic shape as $\cos(x)$ though its initial value has changed to be $\cos(C)$.

Check the box to show points on the graph and arrows on the diagram for the function $ h(x) = \cos( x-C)$.
Move the slider to change the function to $\sin$ or $\tan$.