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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 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.