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Asymptotes definitions Flashcards

Asymptotes definitions
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  • Asymptote

    A line that a rational function graph approaches infinitely close but never touches, shaping the graph's behavior at extremes or near undefined points.
  • Rational Function

    A function expressed as the ratio of two polynomials, often exhibiting unique features like asymptotes and holes.
  • Horizontal Asymptote

    A horizontal line indicating the y-value a rational function approaches as x moves toward positive or negative infinity.
  • Vertical Asymptote

    A vertical line where a rational function becomes undefined, causing the graph to shoot up or down without bound near specific x-values.
  • Hole

    A point of discontinuity on a rational function's graph, marked by an open circle, resulting from a canceled common factor.
  • Removable Discontinuity

    A gap in a rational function's graph at a specific x-value, caused by a factor that cancels from both numerator and denominator.
  • Domain

    The set of all possible x-values for which a rational function is defined, excluding values causing division by zero.
  • Range

    The set of all possible y-values a rational function can output, influenced by horizontal asymptotes and holes.
  • Leading Coefficient

    The coefficient of the term with the highest degree in a polynomial, crucial for determining horizontal asymptotes.
  • Degree

    The highest exponent of the variable in a polynomial, used to compare numerator and denominator for asymptote analysis.
  • Lowest Terms

    A simplified form of a rational function where all common factors between numerator and denominator are canceled.
  • Dashed Line

    A graphical representation used to indicate the location of an asymptote on a rational function's graph.
  • End Behavior

    The trend of a rational function's graph as x approaches infinity or negative infinity, often dictated by horizontal asymptotes.
  • Common Factor

    A polynomial expression present in both the numerator and denominator, whose cancellation may create a hole.
  • Arrow Notation

    A symbolic way to describe how a function behaves as x approaches certain values, especially near asymptotes.