APFIVE Vertical Asymptotes and Holes
Which statement correctly identifies the vertical asymptote(s) and/or hole(s) of the rational function $$r(x)=\frac{x-2}{(x-2)^2}$$?
A
There is both a vertical asymptote and a hole at $$x=2$$.
B
There is a vertical asymptote at $$x=2$$ because the factor $$x-2$$ cancels partially (the numerator cancels one instance) leaving an uncanceled factor in the denominator.
C
The function is defined at $$x=2$$, so it has neither a hole nor a vertical asymptote.
D
There is a hole at $$x=2$$ because the factor cancels completely.
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