Short Answer 
The first step involves rewriting the function by factoring out -8, leading to a transformation that yields -2 before the radical. Next, the graph reflects over both the x-axis and y-axis due to the negative factors, and finally, it undergoes a vertical stretch by a factor of 2 and a translation of ¬Ω unit to the left.
Step 1: Rewrite the Function
To understand the transformation of the parent function, start by rewriting the given function. Focus on factoring out the number that influences the radical’s output. In this case, factor -8 from the radicand. By doing this, take the cube root to reposition the constant in front of the radical, ultimately yielding a result of -2 before the radical symbol.
Step 2: Analyze Reflections
Next, examine how the function’s graph transforms in relation to the parent function. The following transformations occur:
- The graph reflects over the x-axis due to the negative sign.
- The graph also reflects over the y-axis because of another negative factor within the equation.
These reflections result in a graph that is flipped both vertically and horizontally compared to the original.
Step 3: Assess Stretch and Translation
Finally, identify the vertical stretch and translation of the graph. The graph is vertically stretched by a factor of 2, meaning its height is increased. Additionally, it is translated ¬Ω unit to the left, affecting the position of the entire graph along the x-axis. These changes give the graph its final transformation from the parent function.