Monotonicity, symmetry, or parity analysis of a trigonometric function
The question asks to determine intervals of increase/decrease, axes of symmetry, centers of symmetry, or even/odd properties of a trigonometric function, or to find extremal domains/values related to these properties.
In the interval $( - 2 \pi , 0 )$, the function $f ( x ) = \sin \left( \frac { 1 } { x ^ { 3 } } \right)$ (A) never changes sign (B) changes sign only once (C) changes sign more than once, but finitely many times (D) changes sign infinitely many times
In the interval $( 0,2 \pi )$, the function $\sin \left( \frac { 1 } { x ^ { 3 } } \right)$ (a) never changes sign (b) changes sign only once (c) changes sign more than once, but finitely many times (d) changes sign infinitely many times.
In the interval $( 0,2 \pi )$, the function $\sin \left( \frac { 1 } { x ^ { 3 } } \right)$ (a) never changes sign (b) changes sign only once (c) changes sign more than once, but finitely many times (d) changes sign infinitely many times.