Transformations either moves, resizes, or reflects a function: Translation, dilation, reflection. etc

Horizontal translations:

y=f(x) into the form   y = f(x ± k). If k>0, it translates the function left by k units, if k<0, it translates the function right by k units.

Vertical translations:

 y = f(x) into the form f(x) ± k. If k>0, the function moves up by k units, if k<0, the function moves down by k units.

Horizontal dilation:

y=f(x) changes into  y = f(kx).

If k>1, the graph shrinks, if 0<k<1, the x values will be stretched into (k,y)

Vertical dilation:

y=f(x) changes ino y=kf(x).

If k>1, the graph stretches into x,k

If 0<k<1, the graph shrinks.

Reflections:

y=f(x) to y=-f(x) with respect to the x axis

y=f(x) to y=f(-x) with respect to the y axis