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Curve Sketching definitions

컨트롤 버튼이 '내비게이션' 모드로 변경되었습니다.
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  • Domain
    Set of all possible input values for which a function is defined, often spanning from negative to positive infinity for polynomials.
  • X-intercept
    Point where a graph crosses the horizontal axis, found by setting the function equal to zero and solving for the variable.
  • Y-intercept
    Point where a graph crosses the vertical axis, determined by evaluating the function at zero.
  • Asymptote
    Line that a graph approaches but never touches; absent in basic polynomial graphs.
  • Symmetry
    Property describing whether a graph mirrors across an axis or the origin, checked by substituting negative inputs.
  • First Derivative
    Expression indicating the rate of change of a function, used to identify intervals of increase or decrease.
  • Critical Point
    Location where the first derivative equals zero or is undefined, marking potential extrema or inflection.
  • Sign Chart
    Table or diagram used to organize intervals and test values to determine where a function increases or decreases.
  • Second Derivative
    Expression describing the curvature of a function, revealing concavity and possible inflection points.
  • Concavity
    Shape characteristic of a graph, indicating whether it bends upward like a smile or downward like a frown.
  • Inflection Point
    Location where a graph changes concavity, found where the second derivative equals zero or is undefined.
  • Local Maximum
    Peak point on a graph where the function changes from increasing to decreasing, identified via derivative sign change.
  • Local Minimum
    Valley point on a graph where the function changes from decreasing to increasing, marked by a derivative sign change.
  • First Derivative Test
    Method using sign changes of the first derivative around critical points to classify extrema.
  • Factoring
    Process of rewriting a polynomial as a product of simpler expressions, aiding in finding intercepts and critical points.