Front

y = f (x+a)

Back

moves the graph of the parent function left "a" units

Front

y = f (x-a)

Back

moves the graph of the parent function right "a" units

Front

y = f(x) + a

Back

moves the graph of the parent function up "a" units

Front

y = f(x) - a

Back

moves the graph of the parent function down "a" units

Front

y = f(ax)

Back

Front

y = a f(x)

Back

If "a" is greater than 1 vertical stretch by a factor of

"a"

OR

If "a" is in between 0 and 1, vertical compression by a factor of

"a"

Front

y = f(-x)

Back

reflection(flip) across y-axis

Front

y = -f(x)

Back

reflection(flip) over x-axis