Identify which of the twelve basic functions listed below fit the description given.
-The four functions whose graphs look the same turned upside down
A) $y = \sin x , y = \cos x , y = x , y = x ^ { 3 }$
B) $y = x , y = x ^ { 3 } , y = \frac { 1 } { x } , y = \sin x$
C) $y = x , y = \frac { 1 } { x } , y = \sin x , y = \frac { 1 } { 1 + e ^ { - x } }$
D) $y = x , y = x ^ { 3 } , y = \frac { 1 } { x } , y = \cos x$

Question

Quizplus · Accepted Answer

The functions $y = x$, $y = x^3$, and $y = \frac{1}{x}$ are symmetric with respect to the origin, meaning their graphs look the same when turned upside down. The sine function, $y = \sin x$, does not have this property, but it is included in option B as a distractor. The correct functions based on the symmetry described are $y = x$, $y = x^3$, and $y = \frac{1}{x}$.

Identify Which of the Twelve Basic Functions Listed Below Fit y=sin⁡x,y=cos⁡x,y=x,y=x3y = \sin x , y = \cos x , y = x , y = x ^ { 3 }y=sinx,y=cosx,y=x,y=x3

Identify Which of the Twelve Basic Functions Listed Below Fit $y = \sin x , y = \cos x , y = x , y = x ^ { 3 }$