Summary of Translation, Reflection, Stretching, and Shrinking

For y = f(x) = x³, consider the expression

A (Bx + C)³ + D .

The constants A, B, C, and D can be thought of as follows.

A: X-axis reflector (+/-) and
vertical stretcher ( |A| > 1 ) or shrinker ( 0 < |A| < 1 )

B: Y-axis reflector(+/-) and
horizontal shrinker ( |B| > 1 ) or stretcher ( 0 < |B| < 1 )

C: Horizontal shifter (-/+ for à / ß)

D: Vertical shifter (+/- for up/down)