Determine the long-run behavior of the following rational functions. Then, determine their $x$-intercepts, $y$-intercepts, and horizontal/vertical asymptotes, if there are any. Write NONE in any unused blanks. If there is more than one root, list the $x$-intercepts in order from least $x$ coordinate to greatest. Similarly, if there is more than one vertical asymptote, list the asymptotes in order from least to greatest.

a) $y = \dfrac{x + 3}{x + 6}$

Long-run behavior:
A. As $x$ goes to both $+ \infty$ and $-\infty$, $y$ goes to $+\infty$
B. As $x$ goes to both $+ \infty$ and $-\infty$, $y$ goes to 0
C. As $x$ goes to both $+ \infty$ and $-\infty$, $y$ goes to 1
D. As $x$ goes to $+ \infty$, $y$ goes to $+ \infty$, and as $x$ goes to $-\infty$, $y$ goes to $- \infty$

$x$-intercepts:
$($ , $)$
$($ , $)$

$y$-intercept:
$($ , $)$

Horizontal asymptote: $y=$
Vertical asymptote(s):
$x =$
$x =$

b) $y = \dfrac{x + 4}{(x-1)^2}$

Long-run behavior:
A. As $x$ goes to both $+ \infty$ and $-\infty$, $y$ goes to 1
B. As $x$ goes to both $+ \infty$ and $-\infty$, $y$ goes to $+\infty$
C. As $x$ goes to $+ \infty$, $y$ goes to $+ \infty$, and as $x$ goes to $-\infty$, $y$ goes to $- \infty$
D. As $x$ goes to both $+ \infty$ and $-\infty$, $y$ goes to 0

$x$-intercepts:
$($ , $)$
$($ , $)$

$y$-intercept:
$($ , $)$

Horizontal asymptote: $y=$
Vertical asymptote(s):
$x =$
$x =$

c) $h(x) = \dfrac{x^2-4}{x^3+4x^2}$

Long-run behavior:
A. As $x$ goes to both $+ \infty$ and $-\infty$, $y$ goes to 0
B. As $x$ goes to both $+ \infty$ and $-\infty$, $y$ goes to $+\infty$
C. As $x$ goes to $+ \infty$, $y$ goes to $+ \infty$, and as $x$ goes to $-\infty$, $y$ goes to $- \infty$
D. As $x$ goes to both $+ \infty$ and $-\infty$, $y$ goes to 1

$x$-intercepts:
$($ , $)$
$($ , $)$

$y$-intercept:
$($ , $)$

Horizontal asymptote: $y=$
Vertical asymptote(s):
$x =$
$x =$

d) $k(x) = \dfrac{x^2-9}{x^2-3x+2}$

Long-run behavior:
A. As $x$ goes to $+ \infty$, so does $y$, and as $x$ goes to $-\infty$, so does $y$
B. As $x$ goes to both $+ \infty$ and $-\infty$, $y$ goes to 1
C. As $x$ goes to both $+ \infty$ and $-\infty$, $y$ goes to 0
D. As $x$ goes to both $+ \infty$ and $-\infty$, $y$ goes to $+\infty$

$x$-intercepts:
$($ , $)$
$($ , $)$

$y$-intercept:
$($ , $)$

Horizontal asymptote: $y=$
Vertical asymptote(s):
$x =$
$x =$

Hint: