Inverse Trigonometric Functions — Quiz

Question 8 • Precalculus

Which graph represents y is equal to inverse tangent x ?

Answer

Image with description On a coordinate plane, a function approaches y = negative StartFraction pi Over 2 EndFraction, increases through an inflection point at (0, 0), and approaches y = StartFraction pi over 2 EndFraction.

Image with description On a coordinate plane, a function approaches y = negative StartFraction pi Over 2 EndFraction in quadrant 4, increases through an inflection point at (0, 0), and approaches y = StartFraction pi over 2 EndFraction in quadrant 2.

Image with description On a coordinate plane, a function approaches x = negative StartFraction pi Over 2 EndFraction in quadrant 2, has an inflection point at (0, 0), and approaches x = StartFraction pi Over 2 EndFraction in quadrant 4.

Image with description On a coordinate plane, a function approaches x = negative StartFraction pi Over 2 EndFraction in quadrant 3, has an inflection point at (0, 0), and approaches x = StartFraction pi Over 2 EndFraction in quadrant 1.

Explanation

The graph of y = arctan(x) is an increasing curve that passes through (0, 0). As x becomes very negative, y approaches −π/2; as x becomes very positive, y approaches π/2. Those horizontal asymptotes and the increasing shape match choice C.

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