<p>What is the period of the graph of y=2 tan (3pix+4) ?
How do I go about solving this?</p>
<p>The period of tan x is pi. Therefore the period of y = tan (3pi*x) is pi/(3pi) = 1/3. Scaling y by 2 or shifting it by 4 doesn’t change the period, so the period is 1/3.</p>
<p>Ok thank you I got it
So it it was 2tan(pix) the period would be same as 2tan(x) if it is the same? then what difference does pi make?</p>
<p>Not quite - scaling the graph of a periodic function by a constant c (e.g. f(x) → cf(x)) does not change the period of the function.</p>
<p>However, replacing x with cx basically “stretches” the graph horizontally by a factor of 1/c. Might be helpful to get out a graphing calculator and plot functions like y = sin x, y = sin 2x, y = sin .1x on the same window.</p>
<p>oh thank you so much I get it now. I really appreciate your help!
Im applying to MIT too by the way if I get lucky I might get to thank you in person :)</p>