Question

question
find the equation of all vertical asymptotes of the following function.
f(x)=\frac{3 x+1}{5 x+10}
answer
attempt 1 out of 2
no vertical asymptotes
no vertical asymptotes
one vertical asymptote
two vertical asymptotes

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 \(3x + 1\):
\(3\times(-2)+1=-6 + 1=-5
eq0\)

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 (\(x = - 2\))