Answer
$f(x) = -2 + 2~cot~x$
Work Step by Step
When $x = 0$, there is an asymptote. This is the graph for a cotangent function.
The value of the function at $x = \frac{\pi}{4}$ is 2 units more than the value of the function at $x = \frac{\pi}{2}$. This is twice the difference in the standard cotangent function. Therefore, we need to multiply by a factor of 2.
Compared with a standard cotangent function, the y-values are translated downward by 2 units. Therefore we need to include the term -2 in this function.
The equation for this graph is: $f(x) = -2 + 2~cot~x$
