Chapter 4 - Graphs of the Circular Functions - Section 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 172: 41

$f(x) = cot~3x$

When $x = 0$, there is an asymptote. This is the graph for a cotangent function. Compared with a standard cotangent function, the first positive asymptote occurs at $x = \frac{\pi}{3}$ instead of $\pi$. Therefore we need to include the term $3x$ for the angle in the function. The equation for this graph is: $f(x) = cot~3x$