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Graphing Logarithmic Functions definitions

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  • Logarithmic Function
    Inverse of an exponential function, with a graph reflected over the line y = x and a vertical asymptote.
  • Exponential Function
    Function where the variable is in the exponent, serving as the inverse of a logarithmic function.
  • Inverse Function
    A function that reverses another, swapping x and y values and reflecting graphs over y = x.
  • Vertical Asymptote
    A dashed line the graph approaches but never touches, typically at x = 0 or x = h for logarithmic functions.
  • Horizontal Asymptote
    A line the graph approaches as x goes to infinity, such as y = 0 for exponential functions.
  • Reflection
    A transformation flipping the graph over the x-axis, y-axis, or the line y = x, altering its orientation.
  • Transformation
    Any change to a graph, including shifts, stretches, compressions, or reflections, applied to the parent function.
  • Parent Function
    The simplest form of a function, serving as the base for transformations, such as log base 2 of x.
  • Domain
    All possible x-values for which the function is defined, often starting at the vertical asymptote for logarithmic graphs.
  • Range
    All possible y-values a function can take; for logarithmic functions, this is always all real numbers.
  • Ordered Pair
    A set of x and y values representing a point on the graph, often swapped between inverse functions.
  • Base
    The constant in a logarithmic or exponential function that determines the graph's direction and shape.
  • Horizontal Shift
    A transformation moving the graph left or right, determined by the value of h in the function.
  • Vertical Shift
    A transformation moving the graph up or down, determined by the value of k in the function.
  • Test Point
    A specific point used to help plot and transform the graph, often derived from the parent function.