Answer
$$
y=\frac{x-4}{x+1}
$$
we find that :
Asymptotes: $x=-1$ and $y=1$
$x$-intercept: 4, the value when $y= 0$
$y$-intercept: -4, the value when $x= 0$
Work Step by Step
$$
y=\frac{x-4}{x+1}
$$
The value $x=-1$ makes the denominator 0, but not the numerator, so the line $x=-1$ is a vertical asymptotic.
To find a horizontal asymptote, let $ x$ get larger and we find that
$$
y= \lim\limits_{x \to \infty}{\frac{x+1}{x-4}}=1
$$
This means that the line $y=1$ is a horizontal asymptote.
Asymptotes: $x=-1$ and $y=1$
$x$-intercept: 4, the value when $y= 0$
$y$-intercept: -4, the value when $x= 0$
