question\nfind all vertical asymptotes of the following function.\n f(x)=\frac{2 x^{2}-20 x}{3 x-30}…

question\nfind all vertical asymptotes of the following function.\n f(x)=\frac{2 x^{2}-20 x}{3 x-30} \nanswer attempt 1 out of 2

question\nfind all vertical asymptotes of the following function.\n f(x)=\frac{2 x^{2}-20 x}{3 x-30} \nanswer attempt 1 out of 2

Answer

Explanation:

Step1: Simplify the function

Factor numerator and denominator: Numerator: (2x^{2}-20x = 2x(x - 10)) Denominator: (3x-30=3(x - 10)) So (f(x)=\frac{2x(x - 10)}{3(x - 10)}=\frac{2x}{3},x\neq10)

Step2: Analyze vertical asymptotes

A vertical asymptote occurs at (x = a) if (\lim_{x\rightarrow a^{-}}f(x)=\pm\infty) or (\lim_{x\rightarrow a^{+}}f(x)=\pm\infty). Since (f(x)=\frac{2x}{3}) (after canceling non - zero factors for (x\neq10)), and the function (y = \frac{2x}{3}) is a linear function (a polynomial of degree 1). The only point of discontinuity is (x = 10), but (\lim_{x\rightarrow10}f(x)=\frac{2\times10}{3}=\frac{20}{3}) (a finite value).

Answer:

No Vertical Asymptotes