Characteristics of Polynomial Graphs

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What is a polynomial function?

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A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.

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What does the degree of a polynomial indicate?

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The degree of a polynomial indicates the highest power of the variable in the polynomial. It determines the polynomial's end behavior and the maximum number of roots.

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What is the leading coefficient of a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It influences the direction of the graph as x approaches positive or negative infinity.

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What is an interval of increase?

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An interval of increase is a range of x-values where the function's output (y-value) is rising as x increases.

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What is an interval of decrease?

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An interval of decrease is a range of x-values where the function's output (y-value) is falling as x increases.

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What is a local maximum?

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A local maximum is a point on the graph of a function where the function value is higher than all nearby points.

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What is a local minimum?

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A local minimum is a point on the graph of a function where the function value is lower than all nearby points.

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What is an absolute maximum?

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An absolute maximum is the highest point over the entire domain of the function.

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What is an absolute minimum?

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An absolute minimum is the lowest point over the entire domain of the function.

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How can you determine if a polynomial function is even or odd?

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A polynomial is even if f(-x) = f(x) for all x, and odd if f(-x) = -f(x) for all x. Even degree polynomials have symmetric graphs about the y-axis, while odd degree polynomials have symmetric graphs about the origin.