Graphing Polynomial Functions definitions Flashcards
Graphing Polynomial Functions definitions
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Polynomial Function An expression involving variables raised to whole number powers and combined using addition, subtraction, and multiplication. End Behavior The direction a graph heads as x approaches positive or negative infinity, determined by the leading term. Leading Coefficient The coefficient of the term with the highest degree, which influences the graph's end behavior. Degree The highest exponent of the variable in a polynomial, indicating the function's overall shape and turning points. X-Intercept A point where the graph crosses or touches the x-axis, found by solving the function set to zero. Y-Intercept The point where the graph crosses the y-axis, found by evaluating the function at zero. Multiplicity The number of times a particular root occurs, affecting whether the graph crosses or touches the axis at that root. Turning Point A location where the graph changes direction from increasing to decreasing or vice versa. Interval of Unknown Behavior A section between known points on the graph where the function's behavior is not yet determined. Ordered Pair A set of x and y values representing a specific point on the graph. Smooth Curve A continuous, unbroken line connecting plotted points, reflecting the nature of polynomial graphs. Factoring A process of rewriting a polynomial as a product of simpler expressions to find roots or intercepts. Root A value of x that makes the polynomial equal to zero, corresponding to an x-intercept.