Question

for ( f(x)=\frac{-4 x - 1}{-2 x - 7} ), find the vertical and horizontal asymptote.
be sure to write your answer as an equation and use a reduced fraction when necessary. if an asymptote does not exist, write dne.
(a) vertical asymptote:
(b) horizontal asymptote:

Explanation:

Step1: Find vertical asymptote

Set the denominator equal to zero: $-2x - 7=0$.
Solve for $x$: $-2x=7$, so $x =-\frac{7}{2}$.

Step2: Find horizontal asymptote

Since the degree of the numerator and denominator is the same (both degree 1).
The horizontal asymptote is $y=\frac{-4}{-2}=2$.

Answer:

(a) Vertical Asymptote: $x =-\frac{7}{2}$
(b) Horizontal Asymptote: $y = 2$