for symmetry with respect to each axis and to the origin. $$y = \frac { x ^ { 2 } + 2 } { x }$$
A) symmetric with respect to the origin
B) symmetric with respect to the $y$-axis
C) symmetric with respect to the $x$-axis
D) both $\mathrm { B }$ and $\mathrm { C }$
E) no symmetry

Question

Quizplus · Accepted Answer

A function is symmetric with respect to the origin if $f(-x) = -f(x)$. For the given function, $f(x) = \frac{x^2 + 2}{x}$, $f(-x) = \frac{(-x)^2 + 2}{-x} = -\frac{x^2 + 2}{x} = -f(x)$, which confirms symmetry with respect to the origin.

For Symmetry with Respect to Each Axis and to the Origin