Question

where does the graph of the function y = tan(x) have asymptotes?
o at the values of x where cos(x)=0
o at the values of x where sin(x)=0
o at the values of x where cos(x) is undefined
o at the values of x where sin(x) is undefined

Explanation:

Recall the definition of the tangent function $\tan(x)=\frac{\sin(x)}{\cos(x)}$. A rational - function has asymptotes where the denominator is zero. Since the denominator of $\tan(x)$ is $\cos(x)$, the graph of $y = \tan(x)$ has asymptotes at the values of $x$ where $\cos(x)=0$.

Answer:

A. at the values of x where $\cos(x) = 0$