Question

question 6 (1 point)
the graph of ( y = \tan x ) has vertical asymptotes at certain values of ( x ) because the tangent ratio is _ at those values.
( \bigcirc ) a) vertical
( \bigcirc ) b) undefined
( \bigcirc ) c) indeterminate
( \bigcirc ) d) zero

Explanation:

The tangent function is defined as \(y = \tan x=\frac{\sin x}{\cos x}\). Vertical asymptotes occur when the denominator \(\cos x = 0\) (since division by zero is undefined). At \(x=\frac{\pi}{2}+k\pi,k\in\mathbb{Z}\), \(\cos x = 0\) and \(\tan x\) is undefined.

• Option a: "Vertical" is not a property of the tangent ratio value.
• Option c: "Indeterminate" (\(0/0\) form) is not the case here (it's \(non - zero/0\) when \(\cos x = 0\)).
• Option d: When \(\tan x = 0\), \(\sin x=0\) (and \(\cos x

eq0\)), which gives horizontal \(x = k\pi,k\in\mathbb{Z}\) (not vertical asymptotes).

Answer:

B. undefined