Calculus graph

[Naeema F]

Hello. Is it possible for someone to help me with this graph?

The Question:
How would a function, f, be sketched according to the properties?
f(-1)=0, f(0)=2. f ‘(x) > 0 on (-∞, -2) ∪ (-2, 3), f ‘(x) < 0 on (3, ∞).
f “(x) > 0 on (-∞, -2) ∪ (0, 3) ∪ (3,∞), f “(x) < 0 on (-2, 0).
lim x→±∞ f(x) = 2, lim x→-2- f(x) = ∞, lim x→-2+ f(x) = -∞, lim x→3- f(x) = ∞, lim x→3+ f(x) = ∞.

My answer is attached below:

 

[Dr.Peterson]

Everything looks good, so I'll just make a tiny quibble or two ...

First, as you drew it, the second derivative remains negative a little past x=0; you have the inflection point a little too far to the right.

Second, I'd draw in the asymptotes, dotted, just to make sure they look right.

In other words, good work! You don't need help.