This function is the transformation of g (x) = x. The order of transformations is as follows 1)Graph y = x(basic function) (blue) 2)Graph y =1x(shift right by 1) (green) 3)Graph y = 31x(vertical stretch by a factor of 3) (pink) 4)Graph y = -31x(reflection about the x- axis) (dark blue) 5)Graph y = -321x(shift up by 2) (redExample:Use transformations to sketch the graph of f(x) = 3(-x+2)2-1. Plot at least three points on the graph of the basic function and use them to perform the transformations. Draw the transformations one at a time. )
2.6 Operations on functions Suppose two functions f and g are given and their domains are Df and Dg respectively.
Example:Suppose that xxf)(and xxg1)(. Find a) (f-g) (4), b) (f/g)(x) and its domain.
Example:Let 312)(xxxfand 1)(xxxg. Find a) (f + g) (1), b) (fg)(x) and its domain Solution :