Question

f is graphed here as the black (solid) prangula and the transformed function g is graphed here as the green (dotted) prangula 1) Decribe the sequence of transformations from f to g2) use function notation to write g in terms of f

Answer 1

Notice that we can make an intermediate step between both graphs by moving the green graph three units to the left:

Notice that the horizontal lengths of the red graph and the blue graph are the same, but all the vertical lengths seem to have been multiplied by 2.

Since the blue graph (black, in the text) is called f and the transformation that takes the graph of f to the red graph is "multiplying by 2", then, the red graph is given by the expression:

`2\cdot f(x)`

Since the green graph is a three-units shift to the right of the red graph, then it is given by the expression:

`2\cdot f(x-3)`

Since the function whose graph is the green graph is called g, then:

`g(x)=2\cdot f(x-3)`

Therefore:

1) The sequence of transformation that takes f to g is:

1.- A stretching in the y-direction by a factor of 2.

2.- A 3-units shift to the right.

2) In function notation, g is given in terms of f by: g(x) = 2f(x-3).