question\nfind the equation of all vertical asymptotes of the following function.\n f(x)=\frac{2…

question\nfind the equation of all vertical asymptotes of the following function.\n f(x)=\frac{2 x-6}{x^{2}-4 x-12}

question\nfind the equation of all vertical asymptotes of the following function.\n f(x)=\frac{2 x-6}{x^{2}-4 x-12}

Answer

Explanation:

Step1: Factor numerator and denominator

Numerator: (2x - 6=2(x - 3)) Denominator: (x^{2}-4x - 12=(x - 6)(x + 2)) So (f(x)=\frac{2(x - 3)}{(x - 6)(x + 2)})

Step2: Find vertical asymptotes

Vertical asymptotes occur where the denominator is zero (and numerator is non - zero). Set denominator ((x - 6)(x + 2)=0), then (x=6) or (x=-2) Check numerator at (x = 6): (2(6 - 3)=6\neq0) Check numerator at (x=-2): (2(-2 - 3)=-10\neq0)

Answer:

Two Vertical Asymptotes ((x = 6) and (x=-2))