The correct option is Option D: The graph is symmetric about origin.
What is the arctan function?
The function f(x) = arctan x is the inverse of tangent function y=tanx.
Checking all the options
Option A: This option is incorrect as the domain of arctan x is real number R i.e. (-∞,∞). arctan x is valid for all values of x between -∞ to ∞.
Option B: This option is incorrect as the range of the function arctan x is (-π/2, π/2) which is the restricted domain of the tan x.
Option C: This option is incorrect as the graph is continuous in R and also bounded in (-π/2, π/2) so it has no vertical asymptotes. But tan x has vertical asymptotes.
Option D: This option is correct as from the graph it is also clear that this function arctan x is symmetric about the origin. Also, function arctan x is an odd function. As odd functions are symmetric about origin, arctan x is symmetric about the origin.
Therefore The correct option is Option D: The graph is symmetric about origin.
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