Which of the following is the function for the graph below and shows the end behavior of the function as x>-00?

Assuming you want x to approach negative infinity, you have the correct answer. It is choice A.

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Explanation:

The root x = -2 leads to the factor x+2. That means the answer is between A and B.

As x approaches negative infinity, i.e. as we move to the left, we're going down the red curve and y = f(x) is going to approach negative infinity as well.

In terms of symbols, we'd write

Informally, we could say "it falls to the left" as a way to describe this left end behavior.

a is the right answer