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f(x)+c
vertical up translation
f(x)-c
vertical down translation
f(x-c)
horizontal right translation
f(x+c)
horizontal left translation
-f(x)
(change y variables) translation across the x-axis
f(-x)
(change x variables) reflection across the y-axis
-f (-x)
(all variables change, same as rotating 180 degrees) reflection across the origin
c·f(x)
vertical dilation
c·f(x) c > 1
vertical dilation stretch(y variables are affected)
c·f(x) c < 1
vertical dilation shrink (x variables are affected)
f(x/c)
horizontal dilation
f(x/c) c > 1
horizontal dilation stretch (the x variables is being affected)
f(x/c) c<1
horizontal dilation shrink (the y variables is being affected)