Martin Flashman, Feb. 19, 2017. Created with GeoGebra

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 functions
change 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 is increasing (pointing up) or
decreasing (pointing down).

Notice how the graph and mapping diagram visualize the fact that for the
general trigonometric function has the same basic shape as core
function though its period has changed to $2\pi/B$, extremes have
changed to $\pm|A|$ for the sine and cosine.

Check the box to show points on the graph and arrows on the diagram
for the function $ f(x) =2\cdot trig( 2x+\frac{\pi}2)$.

Move the slider to change the function to $\cos$ or $\tan$ or the
values of $A, B,$ or $C$ which you can also enter manually.