Given the Green graph f(x) determine and describe the transformation needed to become the Purple graph:

Question

Write the transformation in the form fx=afbx-c+d to change from the Green to Purple graph.
Describe the transformation in terms of direction and type (for example vertical translation up by

Answer 1

To transform the Green graph to the Purple graph using the transformation fx=afbx-c+d, several changes need to be made:

1. Vertical translation up by 2 units: This can be achieved by adding 2 to the function, so fx = f(x) + 2.

2. Horizontal stretch by a factor of 2: This can be achieved by multiplying the input (x) by 2, so fx = f(2x) + 2.

Thus, the transformation from the Green graph to the Purple graph can be described as:
fx = f(2x) + 2.