# How do you find the end behavior of #y = 2x^3-3x^2+4x+1#?

The end behavior of a function is the behavior of the function as x approaches positive infinity or negative infinity.

So we have to do these two limits:

and

Than:

and

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To find the end behavior of the function ( y = 2x^3 - 3x^2 + 4x + 1 ), you examine the leading term, which is ( 2x^3 ).

As ( x ) approaches positive infinity, ( 2x^3 ) also approaches positive infinity, and as ( x ) approaches negative infinity, ( 2x^3 ) approaches negative infinity.

Therefore, the end behavior of the function is as follows:

- As ( x ) approaches positive infinity, ( y ) approaches positive infinity.
- As ( x ) approaches negative infinity, ( y ) approaches negative 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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