Question

What transformation of the parent function f(x) is made to get -f(x - 2) - 3?

A. a reflection in the x-axis, -2 units in the x-direction, 3 units in the y-direction
B. a reflection in the x-axis, 2 units in the x-direction, 3 units in the y-direction d
C. a reflection in the x-axis, -2 units in the x-direction, -3 units in the y-direction
D. a reflection in the x-axis, 2 units the x-direction, -3 units in the y-direction

Answer 1

The transformation of the parent function f(x) to get -f(x - 2) - 3 is a reflection in the x-axis, 2 units in the x-direction, -3 units in the y-direction.

Step-by-step explanation:

The transformation of the parent function f(x) to get -f(x - 2) - 3 is:

A reflection in the x-axis, 2 units in the x-direction, 3 units in the y-direction.

This can be broken down into the following steps:

1. Start with the parent function f(x).
2. Reflect the function in the x-axis to get -f(x).
3. Translate the function 2 units in the positive x-direction to get -f(x - 2).
4. Translate the function 3 units in the negative y-direction to get -f(x - 2) - 3.

So, the correct choice is option D: a reflection in the x-axis, 2 units in the x-direction, -3 units in the y-direction.