graph transformations

y = f(x) + a

what happens, describe transformation (+ vector)

way to remember?

a is separate, flies away

( 0 )

( a )

translation up by a

y = f(x+ a)

what happens, describe transformation (+ vector)

way to remember?

bracket is lengthened horizontally

( - a )

( 0 )

translation to the LEFT by a

y = a . f(x)

what happens to x/y, describe transformation

way to remember?

vertical stretch (enlargement)

(same x, [y x a])

y and a are close, y is changed x a

y = f(x . a)

horizontal stretch by factor 1/a (enlargement)

brackets are lengthened horizontally

a and x are close, x is changed

(divide x by a), y

y = - f(x)

— closer to y, y changes

reflection in x axis

M

___

W

y = f(-x)

— is closer to x, x is changed

reflection in y axis

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