Question

Suppose the function f(x) is transformed and the new rule for the translated function, g(x), is g(x) = f(x -7) - 11. Describe this transformation.

Answer 1

The transformation of function f(x) by g(x) = f(x -7) - 11 involves a horizontal shift 7 units to the right and a vertical shift 11 units down.

Step-by-step explanation:

When analyzing function transformations, we have certain rules that determine how the graph of a function is altered. For the translated function g(x) given by g(x) = f(x -7) - 11, we see two transformations applied to the function f(x). The first part of the transformation, f(x - 7), indicates a horizontal shift of the graph of f(x) by 7 units to the right.

This is because when we have f(x - d), it represents a shift to the right by d units. The second part of the transformation, - 11, reflects a vertical shift downwards by 11 units. Therefore, the described transformation of the function f(x) involves moving the original graph 7 units to the right and 11 units down to get the graph of g(x).