Understanding Polynomial Functions definitions Flashcards
Understanding Polynomial Functions definitions
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Polynomial Function An expression with only positive whole number exponents, written as f(x), and always produces a smooth, continuous graph. Standard Form A way of writing polynomials with terms in descending order of exponents, combining like terms for clarity. Leading Coefficient The coefficient attached to the term with the highest exponent in a polynomial, crucial for determining end behavior. Degree The highest exponent present in a polynomial, which influences the graph's shape and number of turning points. End Behavior The direction a polynomial graph heads as x approaches positive or negative infinity, determined by degree and leading coefficient. Domain The set of all real numbers for which a polynomial function is defined, always spanning from negative to positive infinity. Zero A value of x where the polynomial equals zero, corresponding to an x-intercept on the graph. Multiplicity The number of times a particular factor appears in a polynomial, affecting how the graph interacts with the x-axis at that 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 in the function's curve. Local Minimum A point on the graph lower than all nearby points, representing the bottom of a valley in the function's curve. Smooth Curve A graph feature of polynomials, indicating no sharp corners or cusps, ensuring a gentle, unbroken path. Continuous Graph A property of polynomial graphs where there are no breaks, holes, or gaps throughout the domain. X-Intercept A point where the graph crosses or touches the x-axis, found by solving f(x) = 0.