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positive graphs
quadratic = smiley
cubic = uphill
quartic = W
negative graphs
quadratic = sad
cubic = downhill
quartic = M
f(x)+d
vertical translation up by d units
f(x+d)
horizontal translatoin left by d units
-f(x)
reflection in the x-axis
f(-x)
reflection in the y-axis
af(x)
vertical stretch/compression (multiply y coordinates by a)
f(ax)
horizontal compression/stretch (multiply x coordinates by 1/a)
how to find asymptotes of reciprocal graph
a fraction never equals zero
a denominator is never zero