Transformation of functions Order of Operations
Horizontal shifts
horizontal stretching/shrinking
reflections over y-axis
reflections over x-axis
vertical stretching/shrinking
vertical shifts
y = cf(x)
if c >1 the graph of y=cf(x) is __________ ___________ by __________ each of its __-coordinates by c
vertically stretched
multiplying
y
if 0 < c < 1, the graph of y=cf(x) is __________ __________ by ___________ each of its __-coordinates by c
vertically shrunk
y = f(cx)
if c>1, the graph of y = f(cx) is _________ ________ by __________ each of its __-coordinates by c
horizontally shrunk
dividing
x
if 0<c<1, the graph of y = f(cx) is _________ ________ by __________ each of its __-coordinates by c
horizontally stretched
the graph y=f(-x) is the graph of y=f(x) _________ about the ___ _____
reflected
y axis
the graph y=-f(x) is the graph of y=f(x) _________ about the ___ _____
x axis