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Graphing Rational Functions definitions

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  • Rational Function
    An expression formed by dividing one polynomial by another, often resulting in asymptotes and possible holes in its graph.
  • Transformation
    A change applied to a graph, such as shifting, reflecting, or stretching, altering its position or orientation.
  • Reflection
    A flip of a graph over a specific axis, caused by a negative sign inside or outside the function.
  • Horizontal Shift
    A movement of a graph left or right, determined by the value subtracted or added to the input variable.
  • Vertical Shift
    A movement of a graph up or down, determined by a constant added or subtracted outside the function.
  • Vertical Asymptote
    A vertical dashed line on a graph where the function approaches infinity, found by setting the denominator to zero.
  • Horizontal Asymptote
    A horizontal dashed line indicating the value a function approaches as x becomes very large or small.
  • Domain
    The set of all possible input values for which a function is defined, often excluding values causing division by zero.
  • Range
    The set of all possible output values a function can produce, often split by horizontal asymptotes.
  • Set Notation
    A mathematical way to describe collections of numbers, often using unions and parentheses to indicate intervals.
  • Hole
    A point where a function is undefined due to a common factor in the numerator and denominator, resulting in a gap in the graph.
  • 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 zero.
  • Multiplicity
    The number of times a factor appears in a polynomial, affecting whether a graph crosses or touches the axis at an intercept.
  • Interval
    A section of the x-axis between known components like asymptotes and intercepts, used to analyze function behavior.