Determine the function which corresponds to the given graph the asymptote is x=3

The function has a horizontal asymptote at y = 3.
The function has a vertical asymptote at x = -3.
The function has a  vertical intercept of 1.
The function has a zero of x = -2.

Because the function has a zero at x = -2, and a vertical asymptote at x = -3, therefore


Write the function in the form
y = 

As x → ∞, y → k.
Because a horizontal asymptote exists at y = 3, therefore  k = 3.
A vertical intercept exists at y = 1.
The function is
 

 

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