Question

The parent function is (f(x) = √ x). The given function is obtained by applying two transformations:

1. Horizontal compression by a factor of 2 ((f(2x))).
2. Vertical shift downward by 1 unit ((f(2x) - 1)).

Answer 1

The question discusses mathematical function transformations including a horizontal compression by a factor of 2, represented as f(2x), and a vertical shift downward by 1 unit, represented as f(2x) - 1, applied to the parent function f(x) = √ x.

Step-by-step explanation:

The student's question revolves around understanding the transformations applied to a parent function f(x) = √ x. Specifically, the question involves a horizontal compression by a factor of 2, represented by f(2x), and a vertical shift downward by 1 unit, which gives us f(2x) - 1.

Applying the horizontal compression to the parent function means that the function's graph will be squeezed or compressed along the x-axis by a factor of 2. To visualize this, any point on the graph with coordinates (a, √ a) will now be moved to (a/2, √ a). The vertical shift downwards by 1 unit then moves every point on the resulting compressed graph down one unit on the y-axis, so the point (a/2, √ a) will become (a/2, √ a - 1).

Therefore, the transformed function is g(x) = √{(2x)} - 1, which is the result of applying the described transformations to the parent function.