Question

Which functions graph has asymptotes located at the values x=t

Answer 1

The function is to have asymptotes at the line:

$x=\pm n\pi$

The graph will have an asymptote when the denominator is 0.

By this definition, the graph of cos x has no asymptotes.

We know that:

$\sin\pi=0$

Therefore, the functions where sin x is at the denominator will have asymptotes at x = π.

The remaining functions can be written as follows:

$\begin{gathered} \csc x=\frac{1}{\sin x} \\ \tan x=\frac{\sin x}{\cos x} \\ \cot x=\frac{\cos x}{\sin x} \end{gathered}$

Therefore, the functions with the asymptote at x = π are csc x and cot x.

OPTION B is the correct answer.