question\nfind the equation of all vertical asymptotes of the following function.\n f(x)=\frac{3 x+1}{5…

question\nfind the equation of all vertical asymptotes of the following function.\n f(x)=\frac{3 x+1}{5 x+10} \nanswer\nattempt 1 out of 2\nno vertical asymptotes\nno vertical asymptotes\none vertical asymptote\ntwo vertical asymptotes

question\nfind the equation of all vertical asymptotes of the following function.\n f(x)=\frac{3 x+1}{5 x+10} \nanswer\nattempt 1 out of 2\nno vertical asymptotes\nno vertical asymptotes\none vertical asymptote\ntwo vertical asymptotes

Answer

Explanation:

Step1: Find the denominator's zero

Set the denominator (5x + 10=0). Solve for (x): $$ \begin{align*} 5x+10&=0\ 5x&=- 10\ x&=-2 \end{align*} $$

Step2: Check if numerator is zero at (x = - 2)

Substitute (x=-2) into the numerator (3x + 1): (3\times(-2)+1=-6 + 1=-5\neq0)

Since the denominator is zero at (x = - 2) and the numerator is non - zero at (x=-2), (x=-2) is a vertical asymptote.

Answer:

One Vertical Asymptote ((x = - 2))