Answer
$f(x)\,\,has\,no\,\,vertical\,asymptotes\, \\$
Work Step by Step
$f(x)=\frac{x^3 - 10x^2 + 16x}{x^2 - 8x}=\frac{x(x-2)(x-8)}{x(x-8)}\,\\
for\,any\,\,a \\
\lim\limits_{x \to a}f(x)=\lim\limits_{x \to a}\frac{x^3 - 10x^2 + 16x}{x^2 - 8x}=\lim\limits_{x \to a}\frac{x(x-2)(x-8)}{x(x-8)}\,=\lim\limits_{x \to a}x-2\\
which\,is\,defind\,for\,any\,a\in \mathbb{R} \\
since\,the\,limit\,exists\,\\
there\,is\,\,no\,\,vertical\,asymptotes\, \\
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