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Find the range of the function \[f(x) = \frac{x^2 + 14x + 9}{x^2 + 2x + 3},\]as $x$ varies over all real numbers.

 Jul 3, 2020
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f(0) = 3.

 

As x increases, f(x) decreases, but does not reach 1.  So the range of f(x) is [3,1).

 Jul 3, 2020

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