Analyze the function f (x) = - tan 4x. Include:. - Domain and range. - Period. - Two Vertical Asymptotes.

F (x) = - tan 4x

Domain of any tangent function is all real numbers except odd multiplies of pi/2. In this case, 4x cannot be an odd multiple of pi/2.

Dom (f) = 4x = / = kpi/2 where k is an odd integer

Dom (f) = x

The range of any tangent function is all real numbers.

Rng (f) = R

The period of tan Bx is pi/B. Thus, the period of f is pi/4.

The vertical asymptotes occur at x = kpi/8 where k is an odd integer. Thus, two vertical asymptotes are x = pi/8 and x = - pi/8.