APPC Polynomial Review

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What is the end behavior of a polynomial function?

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The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

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Define an even function.

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An even function is a function f(x) that satisfies the condition f(-x) = f(x) for all x in the domain of f. Its graph is symmetric with respect to the y-axis.

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Define an odd function.

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An odd function is a function f(x) that satisfies the condition f(-x) = -f(x) for all x in the domain of f. Its graph is symmetric with respect to the origin.

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What does it mean if a polynomial has a degree of 7?

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A polynomial of degree 7 has its highest exponent as 7. This indicates that the polynomial can have up to 7 roots and its end behavior is determined by the leading coefficient.

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What is the significance of the leading coefficient in a polynomial?

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The leading coefficient of a polynomial determines the direction of the end behavior of the graph. If it is positive, the graph rises to the right; if negative, it falls to the right.

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How do you determine the intervals where a polynomial is less than zero?

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To find where a polynomial f(x) < 0, identify the roots of the polynomial, then test intervals between the roots to see where the polynomial takes negative values.

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What is the limit notation for end behavior?

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This means that as x approaches positive infinity, the value of the function f(x) decreases without bound.

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This means that as x approaches negative infinity, the value of the function f(x) increases without bound.

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