What is the period function of f (x) = 1/2tan (2x+5)

Compare your f (x) = 1/2tan (2x+5) to

g (x) = a*tan (bx + c).

Note how b = 2.

The period of the given tangent function is pi/b, which here is pi/2, or 90 degrees. Multiplying x by 2 horizontallyl compresses the graph of tan x by a factor of 1/2.