BackGraphing Logarithmic Functions definitions
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BackLogarithmic 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.
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