Note : definitely, not HW
Source: Chandler Unified School District ( Review Test , Rational functions, 2013-2014) : https://www.cusd200.org/cms/lib7/IL01001538/Centricity/Domain/1586/Review_for_Rational_Functions_Test_2013-2014.pdf
The graph is :
Let's write the desired equaton as : $\frac {P(x)} {Q(x)}$.
We need 2 vertical asymptotes , at $x=2$ and $x=-3$ . So $Q(x)= ( x-2) (x+3)$.
We need $2$ zeros , at $x=-4$ and $x=-1$. So , let's write $P(x)$ as $ k (x+4) (x+1)$.
Since we need a horizontal asympote $y=2$, let's set $k=2$.
Consequently we arrive at :
$f(x)= \frac {P(x)} {Q(x)} = \frac {2 (x+4) (x+1)} { ( x-2) (x+3)}$.
But that does not work :
(1) The concavity of the middle branch is not oriented to the right side
(2) The left branch follows its asymptote to $- \infty$ while it should increase indefinitely upwards.
What do I miss and what can I do to correct the inadequate features of the curve I obtain?