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Graphing Rational Functions definitions

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  • Rational Function
    An expression formed by dividing one polynomial by another, often exhibiting asymptotes and restricted domains.
  • Transformation
    A change applied to a graph, such as shifting, reflecting, or stretching, altering its position or orientation.
  • Vertical Asymptote
    A dashed line where the graph approaches but never touches, occurring where the denominator equals zero.
  • Horizontal Asymptote
    A dashed line indicating the value a function approaches as x becomes very large or very small.
  • Reflection
    A flip of the graph over the x-axis or y-axis, determined by a negative sign outside or inside the function.
  • Horizontal Shift
    A movement of the graph left or right, determined by the value subtracted from x inside the function.
  • Vertical Shift
    A movement of the graph up or down, determined by a constant added or subtracted outside the function.
  • Domain
    All possible x-values for which the function is defined, often excluding values that make the denominator zero.
  • Range
    All possible y-values the function can take, typically split by horizontal asymptotes.
  • X-intercept
    A point where the graph crosses the x-axis, found by setting the numerator equal to zero.
  • Y-intercept
    A point where the graph crosses the y-axis, found by evaluating the function at x equals zero.
  • Multiplicity
    The number of times a factor appears in the numerator or denominator, affecting how the graph behaves at intercepts.
  • Interval
    A section of the x-axis between key points like asymptotes or intercepts, used to analyze graph behavior.
  • Set Notation
    A mathematical way to describe domain and range, often using symbols like parentheses and union.
  • Leading Coefficient
    The coefficient of the highest degree term in a polynomial, used to determine horizontal asymptotes.