Question

Describe how the graph of the function f(x) = 3 |x| - 2 can be made by transforming the graph of the parent function f(x) = |x|. Which transformation is correct?

A) A vertical stretch by a factor of 3 and translate left 2 units
B) Vertically compressed by a factor of 3 and translate down 2 units
C) Vertically compressed by a factor of 3 and translate left 2 units
D) A vertical stretch by a factor of 3 and translate down 2 units

Answer 1

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.