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Vertical and Horizontal Transformations of Function Graphs in Algebra

How the parameters in $y = k \cdot f(x-h) + v$ move, stretch and reflect the graph of a parent function, and why a negative leading coefficient reflects the graph across the horizontal line it is measured from.

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Graphing Function Transformations in Precalculus Using Shifts and Reflections

Function transformations represent a set of geometric operations applied to parent functions within precalculus and algebraic analysis to generate specific function families via vertical/horizontal s…