Can you please help me with this graphing question? - Printable Version +- Twitist Forums (http://twitist.com) +-- Forum: Instagram (/forum-26.html) +--- Forum: General Instagram (/forum-27.html) +--- Thread: Can you please help me with this graphing question? (/thread-148766.html)

Can you please help me with this graphing question? - 203 - 04-28-2014 01:34 PM 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 - 04-28-2014 01:50 PM 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 -Ï€/2 to Ï€/2 the value of tan x increases So the curve goes on increasing from -Ï€/2 to Ï€/2 We also know,tan(-Ï€/2)=not defined Actually, tan(-Ï€/2)→ -∞ Also we know, tan(Ï€/2)=not defined Actually, tan(Ï€/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(-Ï€/2) is -∞ For the curve y=6tan(x/6), x/6=-Ï€/2 gives x=-3Ï€ Therefore y(-3Ï€)=-∞ (4)We know tan(Ï€/2) is +∞ For the curve y=6tan(x/6), x/6=Ï€/2 gives x=+3Ï€ Therefore y(3Ï€)=+∞ (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 Ï€/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.