Question

Describe the transformation that takes the function f(x) = x to the function g(x) = 1/2x - 11. Specifically, identify the direction and magnitude of any shifts or changes applied to f(x) to obtain g(x).

Answer 1

The transformation involves a vertical stretch or compression and a vertical shift downwards.

Step-by-step explanation:

The transformation that takes the function f(x) = x to the function g(x) = 1/2x - 11 involves both a vertical and a horizontal shift.

To obtain g(x), the original function f(x) is multiplied by 1/2, which represents a vertical stretch or compression. In this case, the function is compressed vertically by a factor of 1/2.

Additionally, the function is shifted downwards by 11 units. This represents a vertical shift in the negative direction.