question find all vertical asymptotes of the following function. f(x)=(x^2 + 8x)/(3x^2 - 75) answer no…

question find all vertical asymptotes of the following function. f(x)=(x^2 + 8x)/(3x^2 - 75) answer no vertical asymptotes no vertical asymptotes one vertical asymptote two vertical asymptotes

question find all vertical asymptotes of the following function. f(x)=(x^2 + 8x)/(3x^2 - 75) answer no vertical asymptotes no vertical asymptotes one vertical asymptote two vertical asymptotes

Answer

Answer:

Two Vertical Asymptotes

Explanation:

Step1: Factor the function

$f(x)=\frac{x(x + 8)}{3(x^{2}-25)}=\frac{x(x + 8)}{3(x - 5)(x + 5)}$

Step2: Find values making denominator 0

Set the denominator $3(x - 5)(x + 5)=0$.

Step3: Solve for x

$x-5 = 0$ gives $x = 5$ and $x+5=0$ gives $x=-5$. So there are two vertical - asymptotes at $x = 5$ and $x=-5$.