Question

Given that f(x) = |x| and v(x) = |-x + 6| - 7, which of the following options accurately describes the transformations that have occurred to change f(x) into v(x)? Please select the correct statement:

A) Vertical stretch by a factor of 7, followed by a horizontal shift 6 units to the left, and finally a vertical shift 7 units downward.
B) Horizontal stretch by a factor of 6, followed by a vertical shift 7 units downward, and then a horizontal shift 7 units to the left.
C) Vertical shift 7 units downward, followed by a horizontal shift 6 units to the left, and finally a vertical stretch by a factor of 7.
D) Horizontal shift 6 units to the left, followed by a vertical shift 7 units downward, and then a horizontal stretch by a factor of 7.

Which option correctly describes the transformations from f(x) to v(x)?"

Answer 1

The correct statement that accurately describes the transformations from f(x) = |x| to v(x) = |-x + 6| - 7 is Option D: Horizontal shift 6 units to the left, followed by a vertical shift 7 units downward, and then a horizontal stretch by a factor of 7.

Step-by-step explanation:

The correct statement that accurately describes the transformations from f(x) = |x| to v(x) = |-x + 6| - 7 is Option D: Horizontal shift 6 units to the left, followed by a vertical shift 7 units downward, and then a horizontal stretch by a factor of 7.

In order to transform f(x) into v(x), we start with a horizontal shift 6 units to the left, which makes the expression inside the absolute value |-x|. Then, we have a vertical shift 7 units downward, represented by - 7 in the expression |-x + 6| - 7. Finally, we have a horizontal stretch by a factor of 7, which is the change in the coefficient of x in the expression |-7x + 6| - 7.