Find all the vertical asymptotes (if any) of the graph of the function $$f ( x ) = \frac { 1 + x } { x ^ { 2 } ( 1 - x ) }$$
A) $x = - 1$
B) $x = 1$
C) $x = 0$
D) $x = 1 , x = 0$
E) no vertical asymptotes

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is zero (and the numerator is not zero at those points). For the given function, $f(x) = \frac{1 + x}{x^2(1 - x)}$, the denominator is $x^2(1 - x)$. Setting this equal to zero gives $x^2 = 0$ and $1 - x = 0$, which leads to $x = 0$ and $x = 1$ as the points where the function is undefined, indicating vertical asymptotes at $x = 0$ and $x = 1$.

Find All the Vertical Asymptotes (If Any) of the Graph f(x)=1+xx2(1−x)f ( x ) = \frac { 1 + x } { x ^ { 2 } ( 1 - x ) }f(x)=x2(1−x)1+x​

Find All the Vertical Asymptotes (If Any) of the Graph $f ( x ) = \frac { 1 + x } { x ^ { 2 } ( 1 - x ) }$