Answer
$$
y=\frac{-2x+5}{x+3}
$$
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 $x= 0$
Work Step by Step
$$
y=\frac{-2x+5}{x+3}
$$
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 $x= 0$
