textbook-theory · English
Stretches and Shifts
A three-page lecture note covering the transformation of functions by vertical and horizontal stretching (scaling) and vertical and horizontal shifting. The document defines each transformation algebraically, illustrates the effects on sine and polynomial examples, and derives the corresponding differentiation rules (constant multiple rule for vertical stretches, chain-rule precursor for horizontal stretches, sum rule for vertical shifts, and substitution rule for horizontal shifts).
function transformationsvertical and horizontal stretchesvertical and horizontal shiftsdifferentiation rules