Understanding Polynomial Functions definitions Flashcards
Understanding Polynomial Functions definitions
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Polynomial Function An expression with positive whole number exponents, written in standard form, whose graph is always smooth and continuous. Standard Form A way of writing expressions with terms in descending order of exponents, combining like terms, and showing the leading coefficient first. Exponent A positive whole number indicating how many times a variable is multiplied by itself in a term. Leading Coefficient The coefficient attached to the term with the highest exponent when the expression is in standard form. Degree The highest exponent present in a polynomial, which determines the function's end behavior and maximum turning points. End Behavior The direction the graph moves as x approaches positive or negative infinity, determined by the leading coefficient and degree. Zero A value of x where the function equals zero, corresponding to an x-intercept on the graph. Multiplicity The number of times a particular factor appears, affecting whether the graph crosses or bounces at a zero. Turning Point A location on the graph where the function changes direction from increasing to decreasing or vice versa. Local Maximum A point on the graph higher than all nearby points, representing the top of a hill. Local Minimum A point on the graph lower than all nearby points, representing the bottom of a valley. X-Intercept A point where the graph crosses or touches the x-axis, found by setting the function equal to zero. Continuous Graph A graph with no breaks or gaps, characteristic of all polynomial functions. Smooth Curve A graph with no sharp corners, always present in polynomial functions. Domain The set of all real numbers for which the function is defined, always from negative infinity to infinity for polynomials.