# What is the end behavior for #F(x)=x^3 -5x+1 #?

Down and up

Since the sign of the leading coefficient is positive and the highest degree is odd (3), then the graph will have an end behavior of down and up (down at the beginning, up at the end).

graph{x^3-5x+1 [-9.455, 10.545, -4.28, 5.72]}

Positive-odd= down-up Negative-odd= up-down Positive-even= up-up Negative-even = down-down

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The end behavior of the function ( F(x) = x^3 - 5x + 1 ) can be determined by observing the leading term of the polynomial, which is ( x^3 ), and its coefficient, which is 1.

As ( x ) approaches positive infinity, the dominant term ( x^3 ) grows without bound. Therefore, the end behavior of the function is that it increases without bound.

As ( x ) approaches negative infinity, the dominant term ( x^3 ) still grows without bound, but in the negative direction. Therefore, the end behavior of the function is that it 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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