# How do you find the end behavior of #9x^4 - 8x^3 + 4x#?

As

graph{9x^4-8x^3+4x [-9.625, 10.375, -2.4, 7.6]} Finding the end behavior is finding what happens as x goes to positive and negative infinity. On the graph, look at the two directions the graph is going: left and right (x) and up and down (y). First lets look at what happens when x goes to positive infinity, the graph is going right (towards positive infinity) and most importantly the graph is also going up (the y values are increasing). This gives the first part of the answer. Now lets look at the negative side the x values are decreasing but the y values are increasing.

This tells us that if you keep putting in negative values the y values will keep going up, hence the second part of the answer.

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To find the end behavior of the polynomial (9x^4 - 8x^3 + 4x), you need to look at the leading term, which is (9x^4). The end behavior of a polynomial is determined by the degree and the leading coefficient of the polynomial.

Since the leading term (9x^4) is a fourth-degree term with a positive leading coefficient (9), the end behavior of the polynomial is as follows:

- As (x) approaches positive infinity ((+\infty)), the polynomial increases without bound.
- As (x) approaches negative infinity ((-\infty)), the polynomial decreases without bound.

Therefore, the end behavior of (9x^4 - 8x^3 + 4x) is that it rises on the right and falls on the left.

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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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