## Calculus with Applications (10th Edition)

$$y=\frac{-2x^{2}-3}{x^{2}-1}$$ has the lines with equations $x= 1$ and $x= -1$ as vertical asymptotic, The line $y=-2$ is a horizontal asymptotic. The y-intercept is 3. This is graph $A$.
$$y=\frac{-2x^{2}-3}{x^{2}-1}$$ The values $x= \pm 1$ makes the denominator 0, but not the numerator, so the lines with equations $$x=1 , \, x=-1$$ as vertical asymptotic. To find a horizontal asymptotic, let $x$ get larger and larger, so that $$y= \lim _{x \rightarrow \infty } \frac{-2x^{2}-3}{x^{2}-1} =- 2.$$ This means that the line $y=-2$ is a horizontal asymptotic. When $x=0$ the y-intercept is 3 This is graph $A$.