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