transformations of graphs

1.  f(x)+a

If a is positive, the graphy move up by +a, if a is negative, the graphy move down by a.

2.  f(x-a)

If a is positive (e.g. f(x-5)) the graph moves a to the left. If a is negative (e.g. f(x--a)) the graph will move right by a.

1.  af(x)

Scale factor stretch of a in y direction. (up and down). Multiplying y coordinate by a.

2.  f(ax)

Scale factor stretch of 1/a in the x direciton. (left and right). Multiply x co-ordinates by 1/a (if a is a fraction, e.g. 1/2, 1/0.5 = 2)

1.  -f(x)

Reflecting in x axis, changing y co-ordinates- multiply all y co-ordinates by -1.

2.  f(-x)

reflecting in y axis, changing x co-ordiantes- multiply all x co-ordinates by -1.