Indice rules

Equation of image and image of y=f(x) for:
translation of Ai+Bj

Equation of image and image of y=f(x) for:
reflection in x-axis

reflection in y-axis

Equation of image and image of y=f(x) for:
Strech factor k in x-direction

Equation of image and image of y=f(x) for:
Stretch scale factor k in y-direction

how to find limit of converging sequence?
A=?
d=?

Binomial expansion