# What is the end behavior of #f(x) = x^3 + 4x#?

To do this, let's take some limits:

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End behavior : Down ( As

Up ( As

and far right portions. Using degree of polynomial and leading

coefficient we can determine the end behaviors. Here degree of

For odd degree and positive leading coefficient the graph goes

graph{x^3 + 4 x [-20, 20, -10, 10]} [Ans]

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The end behavior of ( f(x) = x^3 + 4x ) as ( x ) approaches positive or negative infinity is that the function grows without bound. As ( x ) approaches positive infinity, ( f(x) ) increases without bound, and as ( x ) approaches negative infinity, ( f(x) ) decreases without bound.

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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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