Another Calculus Graphing Problem

Question

Sketch two periods of the graph of the function: p(x)=tan(x-(pi/4)) Identify the stretching factor, period, and asymptotes.

Answer 1

So Jade A.,

You should know at this point what the straight tan graph looks like. Your graph of interest looks exactly the same, but it is offset π / 4 to the right on the x-axis (check that, by substituting that value in for x in the stated function. The argument now evaluates to (π / 4) -(π / 4) which is 0, exactly like the origin point on the straight tan graph). So the stretching factor is the same as for the straight tan graph (I'll assume that means =1?), the period is unchanged from straight tan, and the asymptotes are just moved (π / 4) to the right from those of straight tan.

So, your strategy on these problems should be, "what do I have to do to x, in order to exactly result in the curve that I know already?"

-- Cheers, --Mr. d.