Question

Can someone please explain how to graph the function y=tan(x-pi/6). I am confused with the phase shift involving pi.

Answer 1

because the x term has a coefficient of 1, you are shifting all of tan(x) pi/6 units to the right

Answer 2

In general, if you have

y = A*tan(Bx-C) + D

the phase shift is C/B

and that tells you how to shift the graph right or left

Answer 3

So at what points would the starting and ending values of this tan graph be?

Answer 4

not sure what you mean

Answer 5

the graph of tan(x) goes on forever in both directions along the x axis

Answer 6

I guess a better way to phrase the question is at what points would the asymptotes be for this graph?

Answer 7

well the asymptotes for tan(x) are at x = (pi/2)*n where n is any integer

Answer 8

this is because tan(x) = sin(x)/cos(x)

and cos(x) = 0 when x = (pi/2)*n (n is any integer)

Answer 9

so you would shift everything over (including the asymptotes) pi/6 units to the right to get y=tan(x-pi/6).

Answer 10

Okay I drew it out and I understand it now : )

Answer 11

ok that's great