Can you please help me with this graphing question?

[203]

Sec 4.6, #2. The question says "Graph two periods of the given tangent function"

y = 6 tan (x/6)

And the the question goes on to say "Choose the correct graph of two periods of y = 6 tan (x/6) below"

Answer choices:

A) http://instagram.com/p/lRF07UEsHS/

B) http://instagram.com/p/lRF27UEsHV/

C) http://instagram.com/p/lRF6A-ksHW/

Please explain and show your work

[Sreejath]

The correct option is B)
Here is the steps

Do you remember the curve y=tan x
It is a periodic curve which passes through origin and as we go from -π/2 to π/2 the value of tan x increases
So the curve goes on increasing from -π/2 to π/2
We also know,tan(-Ï€/2)=not defined
Actually,
tan(-π/2)→ -∞
Also we know, tan(Ï€/2)=not defined
Actually,
tan(π/2)→ +∞
Thus we have the curve y=tan x in the interval (-Ï€/2,Ï€/2)

We know y=tan x is periodic with Period T=Ï€
So in order to get the curve y=tan x in the entire range of real numbers,just use it periodic property.
That is, COPY and PASTE the curve in the domain (-Ï€/2,Ï€/2) to other intervals.
................................................................................​.......................................................................
Coming Back to our QUESTION
In order to find the correct option,just use trial and error method

Given,
y=6tan(x/6)

From this we can easily infer the following and using those inferences we can find the correct choice

(1)Observe that y(0)=6tan(0/6)=0
Therefore the curve passes through origin (0,0)

(2)When y=6,
6tan(x/6)=6
tan(x/6)=1
we know, tan(Ï€/4)=1
Therefore, x/6=Ï€/4
x=3Ï€/2
Thus the curve must pass through (3Ï€/2,6)

(3)We know tan(-π/2) is -∞
For the curve y=6tan(x/6),
x/6=-Ï€/2 gives x=-3Ï€
Therefore y(-3π)=-∞

(4)We know tan(π/2) is +∞
For the curve y=6tan(x/6),
x/6=Ï€/2 gives x=+3Ï€
Therefore y(3π)=+∞


(5)Since y=tan x is an increasing curve,y=6tan(x/6) is also an increasing curve


(6)The function Atan(Bx+C) is periodic with period π/B
Thus
y=6tan(x/6) is periodic with period 6Ï€

Using some or all of the above inferences we can see that B) is the correct choice.