Transformations and Parent Functions

Front

f(x) + k

Back

Vertical translation up 'k' units

Front

f(x) - k

Back

Vertical translation down 'k' units

Front

f(x + h)

Back

Horizontal translation left 'h' units

Front

f(x - h)

Back

Horizontal translation right 'h' units

Front

-f(x)

Back

Reflection over x-axis

Front

f(-x)

Back

Reflection over y-axis

Front

af(x) (a > 1)

Back

Vertical stretch by factor of a

Front

af(x) (a is a fraction)

Back

Vertical shrink/compression by factor of a

Front

f(ax) (a > 1)

Back

Horizontal shrink/compression by factor of 1/a

Front

f(ax) (a is a fraction)

Back

Horizontal stretch by factor of 1/a