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Describe the end behavior of each polynomial. (a) y = x3 − 5x2 + 9x − 14

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Answer:

The end behavior of a polynomial refers to the behavior of the polynomial function as x approaches positive infinity or negative infinity.

To determine the end behavior of the polynomial y = x^3 - 5x^2 + 9x - 14, we look at the leading term, which is the term with the highest power of x. In this case, the leading term is x^3.

When the degree of the leading term is odd (in this case, the degree is 3), the end behavior of the polynomial is as follows:

- As x approaches positive infinity, the value of the polynomial also approaches positive infinity.

- As x approaches negative infinity, the value of the polynomial approaches negative infinity.

Therefore, for the polynomial y = x^3 - 5x^2 + 9x - 14, the end behavior is that the graph of the polynomial rises to positive infinity as x approaches positive infinity, and falls to negative infinity as x approaches negative infinity.

It is important to note that the end behavior can vary for different polynomials, depending on the degree and leading term. It is always a good practice to identify the leading term and its degree to determine the end behavior of a polynomial.

Explanation:

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