## Calculus with Applications (10th Edition)

$$y=\frac{-2x+5 }{x+3}$$ We obtain that: Asymptotes: $y=-2$ and $x=-3$ $x$-intercept: $\frac{5}{2}$ the value when $y= 0$. $y$-intercept: $\frac{5}{3}$ the value when $x= 0$
$$y=\frac{-2x+5 }{x+3}$$ The value $x=-3$makes the denominator 0, but not the numerator, so the line $x=-3$ is a vertical asymptote. To find a horizontal asymptote, let $x$ get larger and we obtain : $$y=\lim\limits_{x \to \infty}\frac{-2x+5 }{x+3}=-2$$ This means that the line $y=-2$ is a horizontal asymptote. So, we have: Asymptotes: $y=-2$ and $x=-3$ $x$-intercept: $\frac{5}{2}$ the value when $y= 0$. $y$-intercept: $\frac{5}{3}$ the value when $x= 0$