f(x) + k

Shifts vertically by k upward

Shifts horizontally by k upward

f(x) - k

shifts vertically k downward

shifts horizontally k upward

-f(x)

reflects f(x) in the x-axis

reflects f(x) in the y-axis

f(-x)

f(x+k)

shifts horizontally by k to the left

shifts vertically by k to the left

f(x-k)

shifts horizontally by k to the right

shifts vertically by k to the right

pf(x) when p>1

stretches vertically by a scale factor of p

stretches horizontally by a scale factor of p

f(qx) when q>1

compresses horizontally by a scale factor of 1/q

compresses vertically by a scale factor of 1/q