Graphing Exponential Functions definitions Flashcards
Graphing Exponential Functions definitions
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Exponential Function A mathematical relationship where a constant base is raised to a variable exponent, producing rapid growth or decay. Base The constant value in an exponential expression that is repeatedly multiplied as the exponent changes. Exponent The variable or number indicating how many times the base is used as a factor in an exponential function. Horizontal Asymptote A horizontal line that a graph approaches but never touches, indicating the function's end behavior. Domain The complete set of possible input values (x-values) for which an exponential function is defined, always all real numbers. Range The set of possible output values (y-values) for an exponential function, determined by the position of the asymptote. Parent Function The simplest form of an exponential function, serving 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 the x-axis or y-axis, depending on the sign placement. Horizontal Shift A transformation moving the graph left or right, determined by changes inside the function's exponent. Vertical Shift A transformation moving the graph up or down, determined by values added or subtracted outside the function. Continuous Graph A graph with no breaks or gaps, where every point between two values is included. One-to-One Function A function where each input corresponds to exactly one output, passing the horizontal line test. End Behavior The description of how a function behaves as the input values approach positive or negative infinity. Test Point A specific coordinate used to help plot or transform a graph, often derived from the parent function.
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