16 the function j is given by j(x)=4 + 3tan(1/2x). which of the following gives the vertical asymptotes of…

16 the function j is given by j(x)=4 + 3tan(1/2x). which of the following gives the vertical asymptotes of j? a) x = 1/2+2πk, where k is an integer b) x = π/2+π/2k, where k is an integer c) x = π/2+πk, where k is an integer d) x = π+2πk, where k is an integer 17 the graph of k is increasing and concave up on the interval (π/2,π). which of the following could be k? a) k(x)=tan(x) b) k(x)= - tan(x) c) k(x)=cot(x) d) k(x)= - cot(x) 18 the graph of h is given by h(x)= - 4cot(2x)+3. which of the following statements about h is true?

16 the function j is given by j(x)=4 + 3tan(1/2x). which of the following gives the vertical asymptotes of j? a) x = 1/2+2πk, where k is an integer b) x = π/2+π/2k, where k is an integer c) x = π/2+πk, where k is an integer d) x = π+2πk, where k is an integer 17 the graph of k is increasing and concave up on the interval (π/2,π). which of the following could be k? a) k(x)=tan(x) b) k(x)= - tan(x) c) k(x)=cot(x) d) k(x)= - cot(x) 18 the graph of h is given by h(x)= - 4cot(2x)+3. which of the following statements about h is true?

Answer

Explanation:

Step1: Recall vertical - asymptote formula for tangent function

The tangent function (y = \tan(u)) has vertical asymptotes at (u=\frac{\pi}{2}+\pi k), where (k) is an integer. For the function (j(x)=4 + 3\tan(\frac{1}{2}x)), we set (u = \frac{1}{2}x).

Step2: Solve for (x)

Set (\frac{1}{2}x=\frac{\pi}{2}+\pi k). Multiply both sides of the equation by (2) to get (x=\pi + 2\pi k), where (k) is an integer.

Answer:

D. (x=\pi + 2\pi k), where (k) is an integer