Question

Describe the four transformations for the function: -2f(x-3)-4.

Answer 1

The four transformations for the function -2f(x-3)-4 are reflection about the x-axis, horizontal translation, vertical translation, and vertical stretch or compression.

Step-by-step explanation:

The given function is -2f(x-3)-4.

1. Reflection about the x-axis:
   To reflect a function about the x-axis, we replace f(x) with -f(x). So, -2f(x-3)-4 becomes -2(-f(x-3))-4.
2. Horizontal translation:
   To horizontally translate a function, we replace x with (x-d), where d is the distance of the translation. Thus, -2(-f(x-3))-4 becomes -2(-f(x-3-3))-4.
3. Vertical translation:
   To vertically translate a function, we add or subtract a constant to the function. So, -2(-f(x-3))-4 becomes -2(-f(x-3))-4+h.
4. Vertical stretch or compression:
   To vertically stretch or compress a function, we multiply the function by a constant factor. Hence, -2(-f(x-3))-4+h becomes a(-2(-f(x-3))-4+h), where a is the constant factor.