Short Answer 
The function undergoes three transformations: first, it is reflected over the x-axis by multiplying by -1; second, it is vertically compressed by a factor of 0.4; and finally, it is translated 2 units to the right. The result of these transformations is represented by the function y = -0.4‚Äöao[3]{-x-2}.
Step 1: Reflection Over the X-Axis
The first transformation applied to the function is the reflection over the x-axis. This is achieved by multiplying the function by -1, leading to the expression: y = -sqrt[3]{-x}. This step inverts the values of the function, effectively flipping it around the x-axis.
Step 2: Compression by a Factor of 0.4
The second transformation involves compressing the function vertically by a factor of 0.4. This is done by multiplying the function by 0.4, resulting in the expression: y = -0.4sqrt[3]{-x}. As a consequence, the height of the function’s outputs diminishes, making it appear “squashed.” This compression adjusts the steepness without changing the direction of the graph.
Step 3: Translation 2 Units to the Right
The final transformation is a horizontal translation of the graph. By subtracting 2 from the input variable x, we achieve the expression: y = -0.4sqrt[3]{-x-2}. This means the entire graph moves 2 units to the right, shifting every point horizontally while maintaining the shape of the transformed function.