Graphing Logarithmic Functions definitions Flashcards
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.
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