Answer
no intercept(s), symmetric with respect to the origin.
Work Step by Step
Step 1. For x-intercept(s), let $y=0$, we have $x^4=-1\longrightarrow $ no solution, no y-intercept(s) as we can not let $x=0$,
Step 2. To test for x-axis symmetry, replace $(x,y)$ with $(x,-y)$, we have $-y=\frac{-(x)^4+1}{2(x)^5}$ which is different from the original equation, thus it is not symmetric with respect to the x-axis,
Step 3. To test for y-axis symmetry, replace $(x,y)$ with $(-x,y)$, we have $y=\frac{-(-x)^4+1}{2(-x)^5}$ which is different from the original equation, thus it is not symmetric with respect to the y-axis,
Step 4. To test for origin symmetry, replace $(x,y)$ with $(-x,-y)$, we have $-y=\frac{-(-x)^4+1}{2(-x)^5}$ which is the same as the original equation, thus it is symmetric with respect to the origin.
