Consider the function fx 2 tan4 pi x pi 1 a What is the p

Consider the function: f(x) = 2 tan(4 pi x - pi) + 1 a). What is the period P? b). What is the horizontal translation b? c). What is the phase angle ? d). What is the y-intercept? e). Sketch one cycle of the graph in the interval (b, b + P) and then extend the sketch back to the y-intercept.

Solution

f(x) = 2 tan ( 4pix - pi ) + 1

standard equation is given by

f(x) = A tan (Bx - C ) + D

a) period P = pi/B = pi / 4pi = 1/4

b) horizontal translation b = 1/ 4pi

c) phase shift = C/B = pi / 4pi = 1/4

d) y intercept is the point where graph cuts y axis

y intercept = 1