graph all vertical and horizontal asymptotes of the rational function. f(x)=(-10x + 11)/(-4x - 6)

Explanation:

Step1: Find vertical asymptote

Set denominator equal to 0. $-4x - 6=0$ Solve for $x$: $-4x=6$, so $x =-\frac{6}{4}=-\frac{3}{2}$.

Step2: Find horizontal asymptote

Since degree of numerator and denominator are the same (both 1), divide leading - coefficients. Leading coefficient of numerator is - 10 and of denominator is - 4. $y=\frac{-10}{-4}=\frac{5}{2}$

Answer:

Vertical asymptote: $x =-\frac{3}{2}$, Horizontal asymptote: $y=\frac{5}{2}$