How can functions be transformed?

A function, y = f(x), with y on the vertical axis and x on the horizontal axis, can be transformed by 3 different ways: It can be stretched (or shrunk)If y = f(ax), the function is stretched by a scale factor 1/a parallel to the x-axis.If y = af(x), the function is stretched by a scale factor a parallel to the y-axis.It can be translated (moved)If y - a = f(x) and hence y = f(x) + a, the function is moved a units in the y direction.If y = f(x-a), the function is moved a units in the x direction.It can be reflected If y = f(-x), the function is reflected in the y-axis as all the values of x become negative.If y = -f(x), the function is reflected in the x-axis as all the values of y become negative.