question find the equation of all vertical asymptotes of the following function. f(x) = (3x + 1)/(5x + 10)…

question find the equation of all vertical asymptotes of the following function. f(x) = (3x + 1)/(5x + 10) answer attempt 1 out of 3 no vertical asymptotes

question find the equation of all vertical asymptotes of the following function. f(x) = (3x + 1)/(5x + 10) answer attempt 1 out of 3 no vertical asymptotes

Answer

Explanation:

Step1: Recall vertical - asymptote condition

Vertical asymptotes occur where the denominator of a rational function is zero and the numerator is non - zero. Set the denominator equal to zero. $5x + 10=0$

Step2: Solve the equation for x

Subtract 10 from both sides: $5x=-10$. Then divide both sides by 5. $x=\frac{-10}{5}=-2$ Check the numerator at $x = - 2$: $3(-2)+1=-6 + 1=-5\neq0$

Answer:

$x=-2$