# How do you find horizontal asymptotes for #f(x) = arctan(x)# ?

By definition,

The tangent function has vertical asymptotes

Moreover, the graph of the inverse function

Thus, the vertical asymptotes

Here's a graph of arctan(x):

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To find the horizontal asymptotes for f(x) = arctan(x), we need to analyze the behavior of the function as x approaches positive and negative infinity.

As x approaches positive infinity, arctan(x) approaches π/2. Therefore, the horizontal asymptote is y = π/2.

As x approaches negative infinity, arctan(x) approaches -π/2. Therefore, the horizontal asymptote is y = -π/2.

In summary, the horizontal asymptotes for f(x) = arctan(x) are y = π/2 and y = -π/2.

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