# Chapter 4 - Graphs of the Circular Functions - Section 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 172: 44

$f(x) = -2 + 2~cot~x$

#### 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: $f(x) = -2 + 2~cot~x$

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