Question

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

Answer 1

Answer:

Domain : $x=\frac{\pi}{8},\frac{3\pi}{8},\frac{5\pi}{8},.......$

Range : All real numbers or (-∞,∞)

Period: $\frac{\pi }{4}$

Vertical asymptote = $x=\frac{\pi}{8}$ and $x=\frac{3\pi}{8}$

Step-by-step explanation:

Given: Function : -tan 4x

Domain of the tangent function is defined as the multiple of $\frac{\pi }{2}$

Since the frequency is given as 4

therefore, domain of the function is  $4x=\frac{\pi }{2}$

$x=\frac{\pi}{8}$

Domain : $x=\frac{\pi}{8},\frac{3\pi}{8},\frac{5\pi}{8},.......$

Range : All real numbers or (-∞,∞)

Period of tangent function is given by y=a tan(bx) where period = $\frac{\pi }{b}$

Period: $\frac{\pi }{4}$

Vertical asymptote is at $x=\frac{\pi}{8}$ and $x=\frac{3\pi}{8}$ since the function would be undefined at those points.

or Vertical asymptote :  $\frac{\pi}{8}+\frac{n\pi}{4}$ where n is an integer

Answer 2

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) = {x | 4x =/= kpi/2 where k is an odd integer} 
Dom(f) = {x | x =/= kpi/8 where k is an odd integer} 

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.