Question

Which description best describes the transformation h(x) = -f(x) - 9?

A. Reflection in the x-axis followed by a vertical shift downward by 9 units.
B. Reflection in the y-axis followed by a horizontal shift to the right by 9 units.
C. Vertical stretch by a factor of 9 followed by a reflection in the x-axis.
D. Horizontal compression by a factor of 9 followed by a vertical shift upward by 9 units

Answer 1

The transformation h(x) = -f(x) - 9 is a A)reflection in the x-axis followed by a vertical shift downward by 9 units.

Step-by-step explanation:

The transformation h(x) = -f(x) - 9 involves two main operations on the function f(x). First, there is a reflection across the x-axis due to the negative sign in front of f(x). This changes the sign of all the y-values of f(x), effectively flipping the graph over the x-axis. Second, subtracting 9 from the entire function results in a vertical shift downward by 9 units. This moves the entire graph straight down along the y-axis.

The correct description of the transformation is therefore: A. Reflection in the x-axis followed by a vertical shift downward by 9 units.