Question

graph all vertical and horizontal asymptotes of the rational function.
$f(x) = \frac{-3x^2 - 4}{2x - 3}$

Explanation:

Step1: Find vertical asymptote

Set denominator equal to 0:
$2x - 3 = 0$
Solve for $x$:
$x = \frac{3}{2} = 1.5$

Step2: Check horizontal asymptote

Compare degrees of numerator/denominator:
Degree of numerator ($-3x^2-4$) is 2, degree of denominator ($2x-3$) is 1. Since $2>1$, there is no horizontal asymptote.

Answer:

Vertical asymptote: $x = 1.5$ (a vertical dashed line at $x=1.5$ on the graph)
No horizontal asymptote