Linear Transformation of graphs

Linear transformation of graphs y=c f(b x+a)+d

Let a point on the graph of y=f(x) be (x,y) and the new coordinates of this point on the new graph be (p,q). Then

Comparing (1) and (3),

Making p and q the subject in (4) and (5),

Therefore the steps to do linear transformation are:

Step 1: Translate the graph -a units parallel to the x-axis

Step 2: Scale the graph by a factor of 1/b parallel to the x-axis

Step 3: Scale the graph by a factor of c parallel to the y-axis

Step 4: Translate the graph +d units parallel to the y-axis