Question

Question #41b35

Answer 1

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]}

Answer 2

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.

Answer 3

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`