Question

graph all vertical and horizontal asymptotes of the rational functio
$f(x)=\frac{-3}{4x + 10}$

Explanation:

Step1: Find the vertical asymptote

Set the denominator equal to zero: $4x + 10=0$.
Solve for $x$: $4x=-10$, so $x =-\frac{10}{4}=-\frac{5}{2}$.

Step2: Find the horizontal asymptote

For a rational function $y=\frac{a}{bx + c}$ (where $a,b,c$ are constants and $b
eq0$), since the degree of the numerator ($0$) is less than the degree of the denominator ($1$), the horizontal asymptote is $y = 0$.

Answer:

Vertical asymptote: $x =-\frac{5}{2}$, Horizontal asymptote: $y = 0$