Analytically determine the location of any vertical asymptotes. $f ( x ) = \frac { x - 80 } { x ^ { 2 } + 1800 }$
A) $x = 8.944272$
B) $x = 0.044444$
C) $x = 42.426407$
D) $x = - 42.426407$
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 $f(x) = \frac{x - 80}{x^2 + 1800}$, the denominator $x^2 + 1800 = 0$ has no real solutions because $x^2 = -1800$ cannot be satisfied by any real number $x$. Therefore, there are no vertical asymptotes.

Analytically Determine the Location of Any Vertical Asymptotes f(x)=x−80x2+1800f ( x ) = \frac { x - 80 } { x ^ { 2 } + 1800 }f(x)=x2+1800x−80​

Analytically Determine the Location of Any Vertical Asymptotes $f ( x ) = \frac { x - 80 } { x ^ { 2 } + 1800 }$