###
vertical translation

y=f(x) >>> y=f(x) +k

###
horizontal translation

y=f(x) >>> y=f(x-h)

###
vertical stretch

y=f(x) >>> y=af(x)

If a>1, the graph is stretched by "a"

###
vertical compression

y=f(x) >>> y=af(x)

If 0<a<1, the graph is compressed by a factor of a

###
horizontal stretch

y=f(x) >>> y=f(bx)

If 0<b<1, the graph is stretched by a factor of 1/b

###
horizontal compression

y=f(x) >>> y=f(bx)

If b>1, the graph is compressed by a factor of 1/b

###
reflection across y axis

y=f(x) >>> y=f(-x)

###
reflection across x axis

y=f(x) >>> y= -f(x)

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