Transformations of Absolute Value Functions

Transformations Outside the FunctionPage 1

Vertical transformations occur outside the function. These include vertical translations defined by f(x) + d, and vertical dilations (stretches or compressions) defined by a * f(x). Changes to the 'a' value can also result in reflections across a horizontal line.

Transformations Inside the FunctionPage 5

Horizontal transformations occur inside the function's argument. These include horizontal translations defined by f(x - c), where c > 0 shifts the graph right, and horizontal dilations defined by f(b * x).

Combining TransformationsPage 7

Complex transformations are expressed using the general form g(x) = a * f(b(x - c)) + d. This model allows for multiple transformations (scaling, shifting, and reflecting) to be applied to the parent function simultaneously by adjusting the input and output coordinates.

Writing Equations in Transformation FormPage 9

Students apply knowledge of transformations to construct mathematical functions from descriptive requirements, translating geometric operations into algebraic expressions using the standard transformation form.