question find all vertical asymptotes of the following function. f(x) = (3x² - 108)/(x - 9) answer no…

question find all vertical asymptotes of the following function. f(x) = (3x² - 108)/(x - 9) answer no vertical asymptotes submit answer

question find all vertical asymptotes of the following function. f(x) = (3x² - 108)/(x - 9) answer no vertical asymptotes submit answer

Answer

Answer:

$x = 9$

Explanation:

Step1: Factor the numerator

$3x^{2}-108=3(x^{2} - 36)=3(x + 6)(x - 6)$

Step2: Recall vertical - asymptote condition

Vertical asymptotes occur where the denominator of a rational function is zero and the numerator is non - zero.

Step3: Set the denominator equal to zero

Set $x−9 = 0$. Solving for $x$ gives $x = 9$. When $x = 9$, the numerator $3x^{2}-108=3\times9^{2}-108=3\times81 - 108=243-108 = 135\neq0$. So $x = 9$ is a vertical asymptote.