8. the function h is given by h(x)=tan(x - π). which of the following gives the vertical asymptotes of h…

8. the function h is given by h(x)=tan(x - π). which of the following gives the vertical asymptotes of h? (a) x = π/2 + πk, where k is an integer (b) x = π/2 + 2πk, where k is an integer (c) x = 3π/2 + πk, where k is an integer (d) x = 3π/2 + πk, where k is an integer

8. the function h is given by h(x)=tan(x - π). which of the following gives the vertical asymptotes of h? (a) x = π/2 + πk, where k is an integer (b) x = π/2 + 2πk, where k is an integer (c) x = 3π/2 + πk, where k is an integer (d) x = 3π/2 + πk, where k is an integer

Answer

Explanation:

Step1: Recall the vertical - asymptote of tangent function

The tangent function (y = \tan(u)) has vertical asymptotes at (u=\frac{\pi}{2}+k\pi), where (k\in\mathbb{Z}). For the function (h(x)=\tan(x - \pi)), let (u=x-\pi).

Step2: Set (u) equal to the asymptote formula

Set (x-\pi=\frac{\pi}{2}+k\pi).

Step3: Solve for (x)

Add (\pi) to both sides of the equation (x-\pi=\frac{\pi}{2}+k\pi). We get (x=\frac{\pi}{2}+\pi + k\pi=\frac{\pi + 2\pi}{2}+k\pi=\frac{3\pi}{2}+k\pi), where (k) is an integer.

Answer:

C. (x=\frac{3\pi}{2}+k\pi), where (k) is an integer