Answer
$f(x) = -2~cot~x$
Work Step by Step
When $x = 0$, there is an asymptote. This is the graph for a cotangent function.
Compared with a standard cotangent function, the positive and negative values are reflected about the x-axis, so this is the graph for a negative cotangent function.
The magnitude of the value of the function at $x = \frac{3\pi}{4}$ is 2, which is twice the value of the standard cotangent function. Therefore, we need to multiply by a factor of 2.
The equation for this graph is: $f(x) = -2~cot~x$
