Pre-Calculus 12 · Algebra
Transformations of Functions
The single form a·f(b(x − h)) + k unifies all function transformations. Each parameter does exactly one thing: h shifts horizontally, k shifts vertically, a stretches or reflects vertically, and b stretches or reflects horizontally. Mastering this framework lets students graph any transformed function without memorizing separate rules.
WHAT STUDENTS WILL LEARN
✓Apply translations, reflections, stretches, and compressions to functions
✓Write transformed equations from a description of the transformation
✓Determine the transformations applied from a graph or an equation
✓Apply transformations to absolute value, square root, and other parent functions
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