Transformations definitions Flashcards
Transformations definitions
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Transformation Any manipulation that changes the position or shape of a function's graph, such as reflection, shift, or stretch. Reflection A flip of a graph over a specific axis, resulting in a mirror image and changing the sign of certain values. Shift A movement of a graph horizontally, vertically, or both, relocating every point without altering the graph's shape. Stretch An alteration that expands a graph away from an axis, making it appear taller or wider depending on the direction. Compression A transformation that squeezes a graph toward an axis, making it appear shorter or narrower. Horizontal Shift A translation of a graph left or right, determined by the value inside the function's argument. Vertical Shift A translation of a graph up or down, determined by a value added or subtracted outside the function. Vertical Stretch A transformation that multiplies all y-values by a constant greater than one, making the graph taller. Vertical Compression A transformation that multiplies all y-values by a constant between zero and one, making the graph shorter. Horizontal Stretch A transformation that multiplies the input by a constant between zero and one, spreading the graph wider. Horizontal Compression A transformation that multiplies the input by a constant greater than one, squeezing the graph closer to the y-axis. Domain The complete set of possible input values for a function, which may change after a transformation. Range The complete set of possible output values for a function, which can be altered by transformations. Function Notation A symbolic way to represent transformations, such as f(x-h)+k for shifts or cf(x) for stretches. Combination Transformation A scenario where multiple transformations, like reflection and shift, are applied to a function simultaneously.
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