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 coefficient and degree. Leading Coefficient The coefficient of the term with the highest degree in a polynomial, which influences the graph's end behavior. Degree The highest exponent of the variable in a polynomial, indicating the maximum number of turning points and end behavior. X-Intercept A point where the graph crosses or touches the x-axis, found by setting the polynomial equal to zero. Y-Intercept The point where the graph crosses the y-axis, found by evaluating the polynomial at x equals zero. Turning Point A location on the graph where the function changes direction from increasing to decreasing or vice versa. Multiplicity The number of times a particular root occurs, affecting whether the graph crosses or just touches the x-axis at that root. Interval A range between two points on the x-axis used to analyze unknown graph behavior between known points. Ordered Pair A set of coordinates (x, f(x)) representing a specific point on the graph. Continuous Curve A smooth, unbroken line connecting plotted points, characteristic of polynomial graphs. Factoring The process of expressing a polynomial as a product of simpler polynomials to find roots or x-intercepts. Root A value of x for which the polynomial equals zero, corresponding to an x-intercept. Graph Sketch A visual representation of a polynomial function, showing intercepts, turning points, and end behavior. Unknown Interval A section of the graph between known points where the function's behavior is not immediately clear.
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