## Calculus with Applications (10th Edition)

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