QuestionGraph all vertical and horizontal asymptotes of the rational function $$f(x)=\frac{-6 x-13}{4 x-6}$$

Studdy Solution
To find horizontal asymptotes, compare the degrees of the numerator and the denominator:
- The degree of the numerator $-6x - 13$ is 1. - The degree of the denominator $4x - 6$ is 1.
Since the degrees are equal, the horizontal asymptote is determined by the ratio of the leading coefficients:
$$y = \frac{-6}{4} = -\frac{3}{2}$$
Thus, there is a horizontal asymptote at $y = -\frac{3}{2}$.
The graph of the function $f(x) = \frac{-6x - 13}{4x - 6}$ has a vertical asymptote at $x = \frac{3}{2}$ and a horizontal asymptote at $y = -\frac{3}{2}$.