4
QuizMultiple Choice

Inverse Trigonometric Functions — Quiz

Question 4 • Precalculus

Which statement is true about y is equal to arctan x ?

Answer
A
The range is all real numbers.
B
The graph contains vertical asymptotes.
C
The domain is open paren negative mathrm pi over 2 comma mathrm pi over 2 close paren .
D
The graph is symmetric about the origin.

Explanation

The inverse tangent function is odd: arctan(−x) = −arctan(x). This means its graph is symmetric about the origin, so choice D is true. Its domain is all real numbers, while its range is (−π/2, π/2); it approaches those range endpoints as horizontal asymptotes, not vertical ones.

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