Transformation of Graphs

Transformation of Graphs, is actually much easier than you maybe would have thought. Here are the condensed notes that will let you quickly learn how to change the shape/position of a graph.

F(x) means just a function of x. For the purpose of this post, the F(x) will be x^2. This is just a simple parabola going through 0.

RULE 1
Anything outside of the brackets will affect the position of the graph in the y axis.
E.g. F(x) +1 will cause the graph to move 1 y unit upwards.
F(x) -4 will cause the graph to move 4 y units downwards.

RULE 2
Anything inside of the brackets will cause movement in the x axis.
If it is a + or - e.g. F(x+1) will be movement in the x axis -1 units.
F(x-5) will cause the graph to move 5 units to the right in the x axis.

NOTE - Anything inside of the bracket will do the opposite of what you think it would do. So +1  will move x -1 and, -2 will move x +2. 

RULE 3
Coefficients  of x will cause a stretch in the x axis.
E.g F(2x) will cause a stretch of 1/2 in the x axis.
F(1/4x) will cause a stretch of 4 in the x axis.

Careful: Let the coefficient of x be C. The stretch of the x coordinates will be equal to 1/C.

RULE 4
Any coefficient of the function will cause a stretch in the y axis.
E.g 2F(x) will cause a stretch in the y axis of 2; Causing all y values to be doubled.
1/2F(x) will cause a stretch in the y axis of 1/2; Causing all the y values to be halved.

Hint: You can treat the F(x) as y. This makes it easier to interpret when transforming the graph.
E.g 4F(x) means 4y which is 4 lots of the y values which is a stretch in the y axis of 4.