Transformations definitions Flashcards
Transformations definitions
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Transformation
Any change to a function's graph or equation that alters its position or shape, such as shifting, reflecting, or stretching. 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 increases the distance between points on a graph, making it appear taller or wider. Compression
A transformation that decreases the distance between points on a graph, making it appear shorter or narrower. Horizontal Shift
A movement of a graph left or right, determined by changes inside the function's argument. Vertical Shift
A movement of a graph up or down, determined by changes added outside the function. Horizontal Stretch
A widening of a graph along the x-axis, caused by multiplying the input by a constant between 0 and 1. Vertical Stretch
An elongation of a graph along the y-axis, caused by multiplying the output by a constant greater than 1. Horizontal Compression
A narrowing of a graph along the x-axis, caused by multiplying the input by a constant greater than 1. Vertical Compression
A flattening of a graph along the y-axis, caused by multiplying the output by a constant between 0 and 1. 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 of Transformations
The sequential application of multiple transformations to a function, affecting both its graph and equation.
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