Question

Describe the transformations for g(x) = -1/3|x+6|+2

from its parent function f(x) = |x| using three complete sentences
Please

Answer 1

The given function g(x) = -1/3|x+6|+2 represents a vertically compressed, horizontally shifted 6 units to the left, and vertically shifted 2 units upwards version of the parent absolute value function f(x) = |x|.

Step-by-step explanation:

The given function is g(x) = -1/3|x+6|+2. The parent function f(x) = |x| represents the absolute value function.

To describe the transformations from f(x) to g(x), we can analyze each part of the given function. The coefficient -1/3 reflects a vertical compression by a factor of 1/3. The term |x+6| represents a horizontal shift of 6 units to the left. Finally, the constant term +2 represents a vertical shift of 2 units upwards.

Combining all the transformations, we can say that g(x) = -1/3|x+6|+2 is a vertically compressed, horizontally shifted 6 units to the left, and vertically shifted 2 units upwards version of the parent function f(x) = |x|.