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Graphing Logarithmic Functions definitions Flashcards

Graphing Logarithmic Functions definitions
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  • Logarithmic Function
    Inverse of an exponential function, typically featuring a vertical asymptote and a domain restricted to positive real numbers.
  • Exponential Function
    Function where the variable is in the exponent, serving as the inverse of a logarithmic function.
  • Inverse Function
    A function that reverses the effect of another, such that their graphs are reflections over the line y = x.
  • Vertical Asymptote
    A dashed line on a graph, often at x = 0 for logarithmic functions, which the curve approaches but never touches.
  • Horizontal Asymptote
    A dashed line, often at y = 0 for exponential functions, that the graph approaches as x increases or decreases.
  • Parent Function
    The simplest form of a function in a family, used as the starting point for transformations.
  • Transformation
    An operation such as shifting, reflecting, or stretching that alters the position or shape of a graph.
  • Reflection
    A transformation producing a mirror image of a graph over a specific axis, determined by the sign of coefficients.
  • Horizontal Shift
    A transformation moving the graph left or right, determined by the value added or subtracted inside the function.
  • Vertical Shift
    A transformation moving the graph up or down, determined by the value added or subtracted outside the function.
  • Domain
    The set of all possible input values for a function, for logarithmic functions typically restricted by the asymptote.
  • Range
    The set of all possible output values for a function, for logarithmic functions it is all real numbers.
  • Base
    The constant in a logarithmic or exponential function that determines the rate of growth or decay.
  • Ordered Pair
    A pair of numbers (x, y) representing a point on the graph, often found by plugging values into the function.
  • Test Point
    A specific point calculated and plotted to help sketch the graph of a function, especially after transformations.