# How do you find the end behavior of #f(x) = -2(x-1)(x+3)^3#?

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To find the end behavior of the function (f(x) = -2(x-1)(x+3)^3), you examine the leading term, which is the term with the highest power of (x). In this case, the leading term is (-2(x+3)^3).

Since the highest power of (x) is odd (3), and the coefficient of the leading term is negative (-2), the end behavior of the function is as follows:

As (x) approaches negative infinity, (f(x)) approaches negative infinity (falls to the left). As (x) approaches positive infinity, (f(x)) approaches negative infinity (falls to the left).

Therefore, the end behavior of the function (f(x) = -2(x-1)(x+3)^3) is that it decreases without bound as (x) approaches both negative and positive infinity.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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