Sketch a graph that satisfies the following conditions

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Sketch the graph of an example of a function f(x) that satisfies all of the following conditions:

Here is what I have so far:

Am I on the right track? I think the graph satisfies all of the conditions, but the lines cross at about (2,3)- is that acceptable? I know there are probably a large number of ways to draw this, is there a better way I should be aware of?

EDIT #1

How does this look? Does the graph now satisfy the conditions?

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2 Answers

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You also need to mark the asymptotic points at $(0,-2)$ and $(0,1)$:

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While, you catches all of the conditions, except #3, which is at $(0,-1)$, which is an isolated point.

But your plot has multiple y values for $x \in (0,2)$, which is not right.

What you should do is:

Connect $(2^+, -\infty)$ to $(+\infty, 3)$.

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