Question

State the degree and end behavior of f(x) = 2x3 – 3x – x2 + 1. Explain or show your reasoning

Answer 1

Answer:

Answer:

As x→∞ , f(x)→-∞

As

x→-∞ , f(x)→∞

Step-by-step explanation:

End behavior is determined by the degree of the polynomial and the leading coefficient (LC).

The degree of this polynomial is the greatest exponent, or

3

.

The leading coefficient is the coefficient of the term with the greatest exponent, or

2

.

For polynomials of even degree, the "ends" of the polynomial graph point in the same direction as follows.

Even degree and positive LC:

As x→∞ , f(x)→∞ As x→∞, f(x)→∞

Even degree and negative LC:

As x→−∞ , f(x)→−∞

As

x→∞ , f(x)→−∞

Answer 2

Answer:

As x→∞ , f(x)→-∞

As

x→-∞ , f(x)→∞

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Step-by-step explanation: