Question #41b35

3 Answers
Apr 19, 2015

You know the period is #\pi# because you know the period of #tan(x)# is #pi#, and you know that if a function #f# is periodic with period #T#, also is #alphaf, alpha != 0# because #alphaf(x) = alphaf(x+T)#, this is trivial (it's just multiplication on both sides of the #=# sign).
For the graph, you know it's zero for #x=kpi, k \in \ZZ# and in every zero the tangent has 4 as angular coefficient, an it is #4 for x=pi/4 + kpi, -4 for x=-pi/4+kpi#, and has a polar singularity in #x=pi/2 + kpi#
graph{4*tan(x) [-10, 10, -5, 5]}

Apr 19, 2015

The period is #pi#, because tanx repeats it self in the interval #(-pi/2, pi/2)# and would repeat in successive intervals to (#pi/2,(3pi)/2#).. and so on to the right of the origin and similarly to the left of it.

Apr 19, 2015

I am not sure it helps, but also you can "see" the period of your function considering the coefficient of x (the number in front of it called #k#);
In this case is #k=1# so you have that:
#k=(2pi)/(period)#
If #k=1# then
#period=2pi#