Final answer:
The function f(x) = 3 |x| - 2 is created by applying a vertical stretch by a factor of 3 to the parent function f(x) = |x| and translating it downwards by 2 units. The correct transformation is option D.
Step-by-step explanation:
To describe how the graph of the function f(x) = 3 |x| - 2 is made by transforming the graph of the parent function f(x) = |x|, we analyze the modifications to the parent function. The number 3 in front of the absolute value indicates a vertical stretch by a factor of 3. This means that for any value of x, the distance from the x-axis to the graph is tripled compared to the parent graph f(x) = |x|.
The term -2 at the end of the function indicates a vertical translation downwards by 2 units. Every point on the graph of the parent function is moved down 2 units to create the graph of f(x) = 3 |x| - 2. Therefore, the correct transformation is:
- Option D) A vertical stretch by a factor of 3 and translate down 2 units.