## Calculus with Applications (10th Edition)

$$y=\frac{2}{3+2x}$$ We find that: Asymptotic : $y=0$ and $x=-\frac{3}{2}$ $x$-intercept: non $y$-intercept: $\frac{2}{3}$
$$y=\frac{2}{3+2x}$$ The function is undefined for $x=-\frac{3}{2}$, so the line $x=-\frac{3}{2}$, is a vertical asymptotic.. To find a horizontal asymptotic, let $x$ get larger and larger, so that $$y=\lim _{x \rightarrow \infty} \frac{2}{3+2x}=0$$ This means that the line $y=0$ is a horizontal asymptotic. When $x=0$ the y-intercept is $\frac{2}{3}$. So , Asymptotic : $y=0$ and $x=-\frac{3}{2}$ $x$-intercept: non $y$-intercept: $\frac{2}{3}$