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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.