find all vertical and horizontal asymptotes of the graph of the function. (enter your answers as a comma…

Explanation:

Step1: Find vertical asymptotes

Set the denominator equal to 0: $6x^{2}+x - 5=0$. Factor the quadratic: $(6x - 5)(x + 1)=0$. Solving for $x$ gives $x=\frac{5}{6}$ and $x=-1$.

Step2: Find horizontal asymptotes

Since the degree of the numerator and denominator are the same (both degree 2), divide the leading - coefficients. The leading coefficient of the numerator is 1 and of the denominator is 6. So $y=\frac{1}{6}$.

Answer:

$x=-1,x = \frac{5}{6},y=\frac{1}{6}$