Answer
Intercepts: none.
The graph has origin symmetry.
Work Step by Step
$\left[\begin{array}{ll}
\text{x-intercepts:} & \text{y-intercepts:}\\
0=\frac{x^{4}+1}{2x^{5}} & y=\frac{0^{4}+1}{2(0)^{5}}\\
x^{4}=-1 & undefined\\
none & \\
&
\end{array}\right]$
Intercepts: none.
Test x-axis symmetry: Replace $y$ with $-y$
$-y=\displaystyle \frac{x^{4}+1}{2x^{5}}$ ... different from initial equation
Test y-axis symmetry: Replace $x$ with $-x$
$ y=\displaystyle \frac{(-x)^{4}+1}{2(-x)^{5}}$
$y=\displaystyle \frac{x^{4}+1}{-2x^{5}}$ ... different from initial equation
Test origin symmetry: $x\rightarrow-x$ and $y\rightarrow-y$.
$-y=\displaystyle \frac{(-x)^{4}+1}{2(-x)^{5}}$
$-y=\displaystyle \frac{x^{4}+1}{-2x^{5}}$
$y=\displaystyle \frac{x^{4}+1}{2x^{5}}$ ...same as initial equation